{"id":35266,"date":"2022-04-02T15:31:14","date_gmt":"2022-04-02T10:01:14","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=35266"},"modified":"2022-04-07T11:42:45","modified_gmt":"2022-04-07T06:12:45","slug":"big-ideas-math-algebra-1-answers-chapter-9","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-9\/","title":{"rendered":"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations"},"content":{"rendered":"<p>If you are seeking homework help to complete the chapter 9 Solving Quadratic Equations Questions then stay connected with us. Here we have shared the best solution for your concerns ie., <strong>Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations Pdf<\/strong> Exercise-wise. This guide will aid students in enhancing their problem-solving and subject knowledge skills. You can easily understand the concepts of Ch 9 Solving Quadratic Equations with the help of the BIM Algebra 1 Textbook Solution Key and perform well in various tests. Utilize this Ch 9 Algebra 1 Big Ideas Math Book Answers for exam revision guide and score high in all examinations.<\/p>\n<h2 class=\"entry-title\">Lesson-wise Chapter 9 Solving Quadratic Equations Big Ideas Math Algebra 1 Textbook Solutions<\/h2>\n<p>Big Ideas math book Algebra 1 ch 9 Answer key cover all required preparation materials such as Questions from Exercises 9.1 to 9.6, Chapter Tests, Practice Tests, Cumulative Assessment, Review Tests, etc. By solving all these resources of the BIM Answer Key, you can easily understand each and every concept of Algebra 1 chapter 9 Solving Quadratic Equations. Access and download the needed exercise of the<a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers\/\"><strong> Big Ideas Math Algebra 1 Answers<\/strong><\/a> Ch 9 Solving Quadratic Equations from the below links and ace up your preparation to become a pro at mathematics.<\/p>\n<ul>\n<li><a href=\"#Solving_Quadratic_Equations_Maintaining_Mathematical_Proficiency\">Solving Quadratic Equations Maintaining Mathematical Proficiency &#8211; Page 477<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Mathematical_Practices\">Solving Quadratic Equations Mathematical Practices &#8211; Page 478<\/a><\/li>\n<li><a href=\"#Lesson_9.1_Properties_of_Radicals\">Lesson 9.1 Properties of Radicals &#8211; Page(480-488)<\/a><\/li>\n<li><a href=\"#Properties_of_Radicals_9.1_Exercises\">Properties of Radicals 9.1 Exercises &#8211; Page(485-488)<\/a><\/li>\n<li><a href=\"#Lesson_9.2_Solving_Quadratic_Equations_by_Graphing\">Lesson 9.2 Solving Quadratic Equations by Graphing &#8211; Page(490-496)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_by_Graphing_9.2_Exercises\">Solving Quadratic Equations by Graphing 9.2 Exercises &#8211; Page(494-496)<\/a><\/li>\n<li><a href=\"#Lesson_9.3_Solving_Quadratic_Equations_Using_Square_Roots\">Lesson 9.3 Solving Quadratic Equations Using Square Roots &#8211; Page(498-502)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Using_Square_Roots_9.3_Exercises\">Solving Quadratic Equations Using Square Roots 9.3 Exercises &#8211; Page(501-502)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Study_Skills:_Keeping_a_Positive_Attitude\">Solving Quadratic Equations Study Skills: Keeping a Positive Attitude &#8211; Page 503<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_9.1_\u2013_9.3_Quiz\">Solving Quadratic Equations 9.1 \u2013 9.3 Quiz &#8211; Page 504<\/a><\/li>\n<li><a href=\"#Lesson_9.4_Solving_Quadratic_Equations_by_Completing_the_Square\">Lesson 9.4 Solving Quadratic Equations by Completing the Square &#8211; Page(506-514)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_by_Completing_the_Square_9.4_Exercises\">Solving Quadratic Equations by Completing the Square 9.4 Exercises &#8211; Page(511-514)<\/a><\/li>\n<li><a href=\"#Lesson_9.5_Solving_Quadratic_Equations_Using_the_Quadratic_Formula\">Lesson 9.5 Solving Quadratic Equations Using the Quadratic Formula &#8211; Page(516-524)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Using_the_Quadratic_Formula_9.5_Exercises\">Solving Quadratic Equations Using the Quadratic Formula 9.5 Exercises &#8211; Page(521-524)<\/a><\/li>\n<li><a href=\"#Lesson_9.6_Solving_Nonlinear_Systems_of_Equations\">Lesson 9.6 Solving Nonlinear Systems of Equations &#8211; Page(526-532)<\/a><\/li>\n<li><a href=\"#Solving_Nonlinear_Systems_of_Equations_9.6_Exercises\">Solving Nonlinear Systems of Equations 9.6 Exercises &#8211; Page(530-532)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Performance_Task:_Form_Matters\">Solving Quadratic Equations Performance Task: Form Matters &#8211; Page 533<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Chapter_Review\">Solving Quadratic Equations Chapter Review &#8211; Page(534-536)<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Chapter_Test\">Solving Quadratic Equations Chapter Test &#8211; Page 537<\/a><\/li>\n<li><a href=\"#Solving_Quadratic_Equations_Cumulative_Assessment\">Solving Quadratic Equations Cumulative Assessment &#8211; Page(538-539)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Solving_Quadratic_Equations_Maintaining_Mathematical_Proficiency\"><\/a>Solving Quadratic Equations Maintaining Mathematical Proficiency<\/h3>\n<p><strong>Factor the trinomial.<\/strong><br \/>\nQuestion 1.<br \/>\nx<sup>2<\/sup> + 10x + 25<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nx<sup>2<\/sup> &#8211; 20x + 100<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nx<sup>2<\/sup> + 12x + 36<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nx<sup>2<\/sup> &#8211; 18x + 81<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nx<sup>2<\/sup> + 16x + 64<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nx<sup>2<\/sup> &#8211; 30x + 225<br \/>\nAnswer:<\/p>\n<p><strong>Solve the system of linear equations by graphing.<\/strong><br \/>\nQuestion 7.<br \/>\ny = -5x + 3<br \/>\ny = 2x &#8211; 4<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\ny = \\(\\frac{3}{2}\\)x &#8211; 2<br \/>\ny = &#8211;\\(\\frac{1}{2}\\)x + 5<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ny = \\(\\frac{1}{2}\\)x + 4<br \/>\ny = -3x &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nWhat value of c makes x<sup>2<\/sup> + bx + c a perfect square trinomial?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Mathematical_Practices\"><\/a>Solving Quadratic Equations Mathematical Practices<\/h3>\n<p>Mathematically proficient students monitor their work and change course as needed.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35269\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 1\" width=\"167\" height=\"119\" \/><br \/>\nQuestion 1.<br \/>\nUse the graph in Example 1 to approximate the negative solution of the equation x<sup>2<\/sup> + x &#8211; 1 = 0 to the nearest thousandth.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nThe graph of y = x<sup>2<\/sup> + x &#8211; 3 is shown. Approximate both solutions of the equation x<sup>2<\/sup> + x &#8211; 3 = 0 to the nearest thousandth.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_9.1_Properties_of_Radicals\"><\/a>Lesson 9.1 Properties of Radicals<\/h3>\n<p><strong>Essential Question<\/strong> How can you multiply and divide square roots?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Operations with Square Roots<br \/>\nWork with a partner. For each operation with square roots, compare the results obtained using the two indicated orders of operations. What can you conclude?<br \/>\na. Square Roots and Addition<br \/>\nIs \\(\\sqrt{36}\\) + \\(\\sqrt{64}\\) equal to \\(\\sqrt{36+64}\\)?<br \/>\nIn general, is \\(\\sqrt{a}\\) + \\(\\sqrt{b}\\) equal to \\(\\sqrt{a+b}\\)? Explain your reasoning.<\/p>\n<p>b. Square Roots and MultiplicationIs \\(\\sqrt{4}\\) \u2022 \\(\\sqrt{9}\\) equal to \\(\\sqrt{{4} \\cdot 9}\\)?<br \/>\nIn general, is \\(\\sqrt{a}\\) \u2022 \\(\\sqrt{b}\\) equal to \\(\\sqrt{{a} \\cdot b}\\)? Explain your reasoning.<\/p>\n<p>c. Is \\(\\sqrt{36}\\) &#8211; \\(\\sqrt{64}\\) equal to \\(\\sqrt{36+64}\\)?<br \/>\nIn general, is \\(\\sqrt{a}\\) &#8211; \\(\\sqrt{b}\\) equal to \\(\\sqrt{a-b}\\)? Explain your reasoning.<\/p>\n<p>d. Square Roots and Division<br \/>\nIs \\(\\frac{\\sqrt{100}}{\\sqrt{4}}\\) equal to \\(\\sqrt{\\frac{100}{4}}\\)?<br \/>\nIn general, is \\(\\frac{\\sqrt{a}}{\\sqrt{b}}\\) equal to \\(\\sqrt{\\frac{a}{b}}\\)? Explain your reasoning.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Writing Counter examples<br \/>\nWork with a partner. A counterexample is an example that proves that a general statement is not true. For each general statement in Exploration 1 that is not true, write a counterexample different from the example given.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35270\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 1\" width=\"228\" height=\"131\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you multiply and divide square roots?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nGive an example of multiplying square roots and an example of dividing square roots that are different from the examples in Exploration 1.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nWrite an algebraic rule for each operation.<br \/>\na. the product of square roots<br \/>\nb. the quotient of square roots<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\sqrt{24}\\)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n&#8211;\\(\\sqrt{80}\\)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt{49 x^{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n\\(\\sqrt{49 n^{5}}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 5.<br \/>\n\\(\\sqrt{\\frac{23}{9}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n&#8211;\\(\\sqrt{\\frac{17}{100}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt{\\frac{36}{z^{2}}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt{\\frac{4 x^{2}}{64}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\\(\\sqrt[3]{54}\\)<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n\\(\\sqrt[3]{16 x^{4}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\\(\\sqrt[3]{\\frac{a}{-27}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt[3]{\\frac{25 c^{7} d^{3}}{64}}\\)<br \/>\nAnswer:<\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 13.<br \/>\n\\(\\frac{1}{\\sqrt{5}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n\\(\\frac{\\sqrt{10}}{\\sqrt{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n\\(\\frac{7}{\\sqrt{2 x}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n\\(\\sqrt{\\frac{2 y^{2}}{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n\\(\\frac{5}{\\sqrt[3]{32}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n\\(\\frac{8}{1+\\sqrt{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n\\(\\frac{\\sqrt{13}}{\\sqrt{5}-2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n\\(\\frac{12}{\\sqrt{2}+\\sqrt{7}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 6, how far can you see when your eye level is 35 feet above the water?<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\nThe dimensions of a dance floor form a golden rectangle. The shorter side of the dance floor is 50 feet. What is the length of the longer side of the dance floor?<br \/>\nAnswer:<\/p>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 23.<br \/>\n3\\(\\sqrt{2}\\) &#8211; \\(\\sqrt{6}\\) + 10\\(\\sqrt{2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\n4\\(\\sqrt{7}\\) &#8211; 6\\(\\sqrt{63}\\)<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n4\\(\\sqrt [3]{ 5x }\\) &#8211; 11\\(\\sqrt [3]{ 5x }\\)<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\n\\(\\sqrt{3}\\)(8\\(\\sqrt{2}\\) + 7\\(\\sqrt{32}\\))<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n(2\\(\\sqrt{5}\\) &#8211; 4)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 28.<br \/>\n\\(\\sqrt [3]{ -4 }\\)(\\(\\sqrt [3]{ 2 }\\) &#8211; \\(\\sqrt [3]{ 16 }\\))<br \/>\nAnswer:<\/p>\n<h3><a id=\"Properties_of_Radicals_9.1_Exercises\"><\/a>Properties of Radicals 9.1 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe process of eliminating a radical from the denominator of a radical expression is called _______________.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 1\" width=\"598\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-1.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-1-300x30.png 300w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat is the conjugate of the binomial \\(\\sqrt{x}\\) + 4?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>WRITING<\/strong><br \/>\nAre the expressions \\(\\frac{1}{3} \\sqrt{2 x}\\) and \\(\\sqrt{\\frac{2 x}{9}}\\) equivalent? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 3\" width=\"518\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-3.png 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-3-300x102.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich expression does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35271\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 2\" width=\"478\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-2.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-2-300x38.png 300w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u201312, determine whether the expression is in simplest form. If the expression is not in simplest form,<\/strong> <strong>explain why.<\/strong><br \/>\nQuestion 5.<br \/>\n\\(\\sqrt{19}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 5\" width=\"371\" height=\"39\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-5.png 371w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-5-300x32.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt{\\frac{1}{7}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt{48}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 7\" width=\"510\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-7.png 510w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-7-300x36.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt{34}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{5}{\\sqrt{2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 9\" width=\"548\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-9.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-9-300x45.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 10.<br \/>\n\\(\\frac{3 \\sqrt{10}}{4}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{1}{2+\\sqrt[3]{2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 11\" width=\"531\" height=\"97\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-11.png 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-11-300x55.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 12.<br \/>\n\\(6-\\sqrt[3]{54}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 13\u201320, simplify the expression.<\/strong><br \/>\nQuestion 13.<br \/>\n\\(\\sqrt{20}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 13\" width=\"173\" height=\"107\" \/><\/p>\n<p>Question 14.<br \/>\n\\(\\sqrt{32}\\)<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n\\(\\sqrt{128}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41944\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 15\" width=\"196\" height=\"101\" \/><\/p>\n<p>Question 16.<br \/>\n&#8211;\\(\\sqrt{72}\\)<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n\\(\\sqrt{125b}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 17\" width=\"209\" height=\"108\" \/><\/p>\n<p>Question 18.<br \/>\n\\(\\sqrt{4 x^{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n\\(-\\sqrt{81 m^{3}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 19\" width=\"290\" height=\"104\" \/><\/p>\n<p>Question 20.<br \/>\n\\(\\sqrt{48 n^{5}}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 21\u201328, simplify the expression.<\/strong><br \/>\nQuestion 21.<br \/>\n\\(\\sqrt{\\frac{4}{49}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41947\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 21\" width=\"161\" height=\"132\" \/><\/p>\n<p>Question 22.<br \/>\n\\(-\\sqrt{\\frac{7}{81}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n\\(-\\sqrt{\\frac{23}{64}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41948\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 23\" width=\"175\" height=\"133\" \/><\/p>\n<p>Question 24.<br \/>\n\\(\\sqrt{\\frac{65}{121}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n\\(\\sqrt{\\frac{a^{3}}{49}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-25.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 25\" width=\"167\" height=\"249\" \/><\/p>\n<p>Question 26.<br \/>\n\\(\\sqrt{\\frac{144}{k^{2}}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n\\(\\sqrt{\\frac{100}{4x^{2}}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 27\" width=\"174\" height=\"248\" \/><\/p>\n<p>Question 28.<br \/>\n\\(\\sqrt{\\frac{25 v^{2}}{36}}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 29\u201336, simplify the expression.<\/strong><br \/>\nQuestion 29.<br \/>\n\\(\\sqrt [3]{ 16 }\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41951\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 29\" width=\"171\" height=\"108\" \/><\/p>\n<p>Question 30.<br \/>\n\\(\\sqrt [3]{ -108 }\\)<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n\\(\\sqrt[3]{-64 x^{5}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-31.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 31\" width=\"310\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-31.png 310w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-31-300x103.png 300w\" sizes=\"(max-width: 310px) 100vw, 310px\" \/><\/p>\n<p>Question 32.<br \/>\n&#8211;\\(\\sqrt[3]{343 n^{2}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n\\(\\sqrt[3]{\\frac{6 c}{-125}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-33.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 33\" width=\"199\" height=\"197\" \/><\/p>\n<p>Question 34.<br \/>\n\\(\\sqrt[3]{\\frac{8 h^{4}}{27}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n\\(-\\sqrt[3]{\\frac{81 y^{2}}{1000 x^{3}}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-35.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 35\" width=\"294\" height=\"309\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-35.png 294w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-35-285x300.png 285w\" sizes=\"(max-width: 294px) 100vw, 294px\" \/><\/p>\n<p>Question 36.<br \/>\n\\(\\sqrt[3]{\\frac{21}{-64 a^{3} b^{6}}}\\)<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 37 and 38, describe and correct the error in simplifying the expression.<br \/>\nQuestion 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35272\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 3\" width=\"259\" height=\"105\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41955\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-37.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 37\" width=\"578\" height=\"161\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-37.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-37-300x84.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35273\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-4.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 4\" width=\"335\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-4.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-4-300x172.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 39\u201344, write a factor that you can use to rationalize the denominator of the expression.<\/strong><br \/>\nQuestion 39.<br \/>\n\\(\\frac{4}{\\sqrt{6}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-39.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 39\" width=\"494\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-39.png 494w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-39-300x66.png 300w\" sizes=\"(max-width: 494px) 100vw, 494px\" \/><\/p>\n<p>Question 40.<br \/>\n\\(\\frac{1}{\\sqrt{13 z}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n\\(\\frac{2}{\\sqrt[3]{x^{2}}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-41.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 41\" width=\"524\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-41.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-41-300x64.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><\/p>\n<p>Question 42.<br \/>\n\\(\\frac{3 m}{\\sqrt[3]{4}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n\\(\\frac{\\sqrt{2}}{\\sqrt{5}-8}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-43.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 43\" width=\"528\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-43.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-43-300x66.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 44.<br \/>\n\\(\\frac{5}{\\sqrt{3}+\\sqrt{7}}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 45\u201354, simplify the expression.<\/strong><br \/>\nQuestion 45.<br \/>\n\\(\\frac{2}{\\sqrt{2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-45.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 45\" width=\"153\" height=\"246\" \/><\/p>\n<p>Question 46.<br \/>\n\\(\\frac{4}{\\sqrt{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n\\(\\frac{\\sqrt{5}}{\\sqrt{48}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41960\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-47.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 47\" width=\"190\" height=\"485\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-47.png 190w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-47-118x300.png 118w\" sizes=\"(max-width: 190px) 100vw, 190px\" \/><\/p>\n<p>Question 48.<br \/>\n\\(\\sqrt{\\frac{4}{52}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n\\(\\frac{3}{\\sqrt{a}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-49.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 49\" width=\"150\" height=\"183\" \/><\/p>\n<p>Question 50.<br \/>\n\\(\\frac{1}{\\sqrt{2 x}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n\\(\\sqrt{\\frac{3 d^{2}}{5}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41962\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-51.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 51\" width=\"198\" height=\"340\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-51.png 198w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-51-175x300.png 175w\" sizes=\"(max-width: 198px) 100vw, 198px\" \/><\/p>\n<p>Question 52.<br \/>\n\\(\\frac{\\sqrt{8}}{\\sqrt{3 n^{3}}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n\\(\\frac{4}{\\sqrt[3]{25}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41963\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-53.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 53\" width=\"184\" height=\"213\" \/><\/p>\n<p>Question 54.<br \/>\n\\(\\sqrt[3]{\\frac{1}{108 y^{2}}}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 55\u201360, simplify the expression.<\/strong><br \/>\nQuestion 55.<br \/>\n\\(\\frac{1}{\\sqrt{7}+1}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41964\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-55.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 55\" width=\"275\" height=\"268\" \/><\/p>\n<p>Question 56.<br \/>\n\\(\\frac{2}{5-\\sqrt{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n\\(\\frac{\\sqrt{10}}{7-\\sqrt{2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41965\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-57.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 57\" width=\"308\" height=\"388\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-57.png 308w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-57-238x300.png 238w\" sizes=\"(max-width: 308px) 100vw, 308px\" \/><\/p>\n<p>Question 58.<br \/>\n\\(\\frac{\\sqrt{5}}{6+\\sqrt{5}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n\\(\\frac{3}{\\sqrt{5}-\\sqrt{2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41966\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-59.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 59\" width=\"320\" height=\"295\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-59.png 320w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-59-300x277.png 300w\" sizes=\"(max-width: 320px) 100vw, 320px\" \/><\/p>\n<p>Question 60.<br \/>\n\\(\\frac{\\sqrt{3}}{\\sqrt{7}+\\sqrt{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe time t (in seconds) it takes an object to hit the ground is given by t = \\(\\sqrt{\\frac{h}{16}}\\), where his the height (in feet) from which the object was dropped.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35274\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 5\" width=\"148\" height=\"167\" \/><br \/>\na. How long does it take an earring to hit the ground when it falls from the roof of the building?<br \/>\nb. How much sooner does the earring hit the ground when it is dropped from two stories (22 feet) below the roof?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41967\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-61.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 61\" width=\"567\" height=\"346\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-61.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-61-300x183.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe orbital period of a planet is the time it takes the planet to travel around the Sun. You can find the orbital period P (in Earth years) using the formula P = \\(\\sqrt{d^{3}}\\), where d is the average distance (in astronomical units, abbreviated AU) of the planet from the Sun.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35275\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-6.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 6\" width=\"311\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-6.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-6-300x138.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\na. Simplify the formula.<br \/>\nb. What is Jupiter\u2019s orbital period?<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe electric current I (in amperes) an appliance uses is given by the formula I = \\(\\sqrt{\\frac{P}{R}}\\), where P is the power (in watts) and R is the resistance (in ohms). Find the current an appliance uses when the power is 147 watts and the resistance is 5 ohms.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35276\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 7\" width=\"249\" height=\"190\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41968\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-63.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 63\" width=\"573\" height=\"483\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-63.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-63-300x253.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 64.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou can find the average annual interest rate r (in decimal form) of a savings account using the formula r = \\(\\sqrt{\\frac{V_{2}}{V_{0}}}\\) &#8211; 1, where V<sub>0<\/sub> is the initial investment and V<sub>2<\/sub> is the balance of the account after 2 years. Use the formula to compare the savings accounts. In which account would you invest money? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35277\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-8.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 8\" width=\"300\" height=\"177\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 65\u201368, evaluate the function for the given value of x. Write your answer in simplest form and in decimal form rounded to the nearest hundredth.<\/strong><br \/>\nQuestion 65.<br \/>\nh(x) = \\(\\sqrt{5x}\\); x = 10<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41969\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-65.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 65\" width=\"303\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-65.png 303w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-65-300x244.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><\/p>\n<p>Question 66.<br \/>\ng(x) = \\(\\sqrt{3x}\\); x = 60<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\nr(x) = \\(\\sqrt{\\frac{3 x}{3 x^{2}+6}}\\); x = 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41970\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-67.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 67\" width=\"302\" height=\"566\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-67.png 302w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-67-160x300.png 160w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><\/p>\n<p>Question 68.<br \/>\np(x) = \\(\\sqrt{\\frac{x-1}{5 x}}\\); x = 8<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 69\u201372, evaluate the expression when a = \u22122, b = 8, and c = \\(\\frac{1}{2}\\). Write your answer in simplest form and in decimal form rounded to the nearest hundredth.<\/strong><br \/>\nQuestion 69.<br \/>\n\\(\\sqrt{a^{2}+b c}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41971\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-69.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 69\" width=\"305\" height=\"216\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-69.png 305w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-69-300x212.png 300w\" sizes=\"(max-width: 305px) 100vw, 305px\" \/><\/p>\n<p>Question 70.<br \/>\n\\(-\\sqrt{4 c-6 a b}\\)<br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n\\(-\\sqrt{2 a^{2}+b^{2}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41972\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-71.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 71\" width=\"371\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-71.png 371w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-71-300x196.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/p>\n<p>Question 72.<br \/>\n\\(\\sqrt{b^{2}-4 a c}\\)<br \/>\nAnswer:<\/p>\n<p>Question 73.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe text in the book shown forms a golden rectangle. What is the width w of the text?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35278\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 9\" width=\"259\" height=\"182\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-73.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 73\" width=\"400\" height=\"617\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-73.png 400w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-73-194x300.png 194w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>Question 74.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe flag of Togo is approximately the shape of a golden rectangle. What is the width w of the flag?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35279\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-10.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 10\" width=\"293\" height=\"172\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 75\u201382, simplify the expression.<\/strong><br \/>\nQuestion 75.<br \/>\n\\(\\sqrt{2}\\) &#8211; 2\\(\\sqrt{2}\\) + 6\\(\\sqrt{2}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41974\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-75.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 75\" width=\"379\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-75.png 379w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-75-300x53.png 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/><\/p>\n<p>Question 76.<br \/>\n\\(\\sqrt{5}\\) &#8211; 5\\(\\sqrt{13}\\) &#8211; 8\\(\\sqrt{5}\\)<br \/>\nAnswer:<\/p>\n<p>Question 77.<br \/>\n2\\(\\sqrt{6}\\) &#8211; 5\\(\\sqrt{54}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-77.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 77\" width=\"339\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-77.png 339w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-77-300x183.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/p>\n<p>Question 78.<br \/>\n9\\(\\sqrt{32}\\) + \\(\\sqrt{2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 79.<br \/>\n\\(\\sqrt{12}\\) + 6\\(\\sqrt{3}\\) + 2\\(\\sqrt{6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41976\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-79.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 79\" width=\"431\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-79.png 431w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-79-300x118.png 300w\" sizes=\"(max-width: 431px) 100vw, 431px\" \/><\/p>\n<p>Question 80.<br \/>\n3\\(\\sqrt{7}\\) &#8211; 5\\(\\sqrt{14}\\) + 2\\(\\sqrt{28}\\)<br \/>\nAnswer:<\/p>\n<p>Question 81.<br \/>\n\\(\\sqrt[3]{-81}\\) + 4\\(\\sqrt[3]{3}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41977\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-81.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 81\" width=\"363\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-81.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-81-300x180.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 82.<br \/>\n6\\(\\sqrt[3]{128 t}\\) &#8211; 2\\(\\sqrt[3]{2 t}\\)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 83\u201390, simplify the expression.<\/strong><br \/>\nQuestion 83.<br \/>\n\\(\\sqrt{2}\\)(\\(\\sqrt{45}\\) + \\(\\sqrt{5}\\))<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-83.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 83\" width=\"390\" height=\"248\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-83.png 390w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-83-300x191.png 300w\" sizes=\"(max-width: 390px) 100vw, 390px\" \/><\/p>\n<p>Question 84.<br \/>\n\\(\\sqrt{3}\\)(\\(\\sqrt{72}\\) &#8211; 3\\(\\sqrt{2}\\))<br \/>\nAnswer:<\/p>\n<p>Question 85.<br \/>\n\\(\\sqrt{5}\\)(2\\(\\sqrt{6x}\\) &#8211; \\(\\sqrt{96x}\\))<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41979\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-85.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 85\" width=\"449\" height=\"246\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-85.png 449w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-85-300x164.png 300w\" sizes=\"(max-width: 449px) 100vw, 449px\" \/><\/p>\n<p>Question 86.<br \/>\n\\(\\sqrt{7y}\\)(\\(\\sqrt{27y}\\) + 5\\(\\sqrt{12y}\\))<br \/>\nAnswer:<\/p>\n<p>Question 87.<br \/>\n(4\\(\\sqrt{2}\\) &#8211; \\(\\sqrt{98}\\))<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41980\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-87.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 87\" width=\"498\" height=\"209\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-87.png 498w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-87-300x126.png 300w\" sizes=\"(max-width: 498px) 100vw, 498px\" \/><\/p>\n<p>Question 88.<br \/>\n(\\(\\sqrt{3}\\) + \\(\\sqrt{48}\\)) (\\(\\sqrt{20}\\) &#8211; \\(\\sqrt{5}\\))<br \/>\nAnswer:<\/p>\n<p>Question 89.<br \/>\n\\(\\sqrt[3]{3}(\\sqrt[3]{4}+\\sqrt[3]{32})\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41981\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-89.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 89\" width=\"422\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-89.png 422w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-89-300x178.png 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><\/p>\n<p>Question 90.<br \/>\n\\(\\sqrt[3]{2}(\\sqrt[3]{135}-4 \\sqrt[3]{5})\\)<br \/>\nAnswer:<\/p>\n<p>Question 91.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe circumference C of the art room in a mansion is approximated by the formula C \u2248 \\(\\sqrt\\frac{a^{2}+b^{2}}{2}\\). Approximate the circumference of the room.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35280\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 11\" width=\"324\" height=\"327\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-11.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-11-297x300.png 297w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-11-150x150.png 150w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41982\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-91.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 91\" width=\"528\" height=\"481\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-91.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-91-300x273.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 92.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nDetermine whether each expression represents a rational or an irrational number. Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35281\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-12.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 12\" width=\"303\" height=\"192\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-12.png 303w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-12-300x190.png 300w\" sizes=\"(max-width: 303px) 100vw, 303px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 93\u201398, simplify the expression.<\/strong><br \/>\nQuestion 93.<br \/>\n\\(\\sqrt[5]{\\frac{13}{5 x^{5}}}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41983\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-93.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 93\" width=\"227\" height=\"546\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-93.png 227w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-93-125x300.png 125w\" sizes=\"(max-width: 227px) 100vw, 227px\" \/><\/p>\n<p>Question 94.<br \/>\n\\(\\sqrt[4]{\\frac{10}{81}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 95.<br \/>\n\\(\\sqrt[4]{256 y}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-95.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 95\" width=\"299\" height=\"42\" \/><\/p>\n<p>Question 96.<br \/>\n\\(\\sqrt[5]{160 x^{6}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 97.<br \/>\n\\(6 \\sqrt[4]{9}-\\sqrt[5]{9}+3 \\sqrt[4]{9}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-97.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 97\" width=\"406\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-97.png 406w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-97-300x81.png 300w\" sizes=\"(max-width: 406px) 100vw, 406px\" \/><\/p>\n<p>Question 98.<br \/>\n\\(\\sqrt[5]{2}(\\sqrt[4]{7}+\\sqrt[5]{16})\\)<br \/>\nAnswer:<\/p>\n<p><strong>REASONING<\/strong> In Exercises 99 and 100, use the table shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35282\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 13\" width=\"321\" height=\"213\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-13.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-13-300x199.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nQuestion 99.<br \/>\nCopy and complete the table by (a) finding each sum ( 2 + 2, 2 + \\(\\frac{1}{4}\\), etc. ) and (b) finding each product ( 2 \u2022 2, 2 \u2022 \\(\\frac{1}{4}\\), etc. )<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 99.1\" width=\"599\" height=\"356\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.1.png 599w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.1-300x178.png 300w\" sizes=\"(max-width: 599px) 100vw, 599px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41987\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 99.2\" width=\"550\" height=\"330\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.2.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-99.2-300x180.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 100.<br \/>\nUse your answers in Exercise 99 to determine whether each statement is always, sometimes, or never true. Justify your answer.<br \/>\na. The sum of a rational number and a rational number is rational.<br \/>\nb. The sum of a rational number and an irrational number is irrational.<br \/>\nc. The sum of an irrational number and an irrational number is irrational.<br \/>\nd. The product of a rational number and a rational number is rational.<br \/>\ne. The product of a nonzero rational number and an irrational number is irrational.<br \/>\nf. The product of an irrational number and an irrational number is irrational.<br \/>\nAnswer:<\/p>\n<p>Question 101.<br \/>\n<strong>REASONING<\/strong><br \/>\nLet m be a positive integer. For what values of m will the simplified form of the expression \\(\\sqrt{2^{m}}\\) contain a radical? For what values will it not contain a radical? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-101.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 101\" width=\"572\" height=\"144\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-101.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-101-300x76.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 102.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe edge length s of a cube is an irrational number, the surface area is an irrational number, and the volume is a rational number. Give a possible value of s.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35283\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-14.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 14\" width=\"149\" height=\"117\" \/><br \/>\nAnswer:<\/p>\n<p>Question 103.<br \/>\n<strong>REASONING<\/strong><br \/>\nLet a and b be positive numbers. Explain why \\(\\sqrt{ab}\\) lies between a and b on a number line. (Hint: Let a&lt; b and multiply each side of a &lt; b by a. Then let a &lt; b and multiply each side by b.)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-103.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 103\" width=\"584\" height=\"193\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-103.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-103-300x99.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 104.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that you can rationalize the denominator of the expression \\(\\frac{2}{4+\\sqrt[3]{5}}\\) by multiplying the numerator and denominator by 4 &#8211; \\(\\sqrt[3]{5}\\). Is your friend correct? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 105.<br \/>\nPROBLEM SOLVING<br \/>\nThe ratio of consecutive terms \\(\\frac{a_{n}}{a_{n}-1}\\) in the Fibonacci sequence gets closer and closer to the golden ratio \\(\\frac{1+\\sqrt{5}}{2}\\) as n increases. Find the term that precedes 610 in the sequence.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-105.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 105.1\" width=\"265\" height=\"528\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-105.1.png 265w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-105.1-151x300.png 151w\" sizes=\"(max-width: 265px) 100vw, 265px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-105.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 105.2\" width=\"335\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-105.2.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-105.2-300x126.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><\/p>\n<p>Question 106.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nUse the golden ratio \\(\\frac{1+\\sqrt{5}}{2}\\) and the golden ratio conjugate \\(\\frac{1-\\sqrt{5}}{2}\\) for each of the following.<br \/>\na. Show that the golden ratio and golden ratio conjugate are both solutions of x<sup>2<\/sup> &#8211; x &#8211; 1 = 0.<br \/>\nb. Construct a geometric diagram that has the golden ratio as the length of a part of the diagram.<br \/>\nAnswer:<\/p>\n<p>Question 107.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nUse the special product pattern (a + b)(a<sup>2<\/sup> &#8211; ab + b<sup>2<\/sup>) = a<sup>3<\/sup> + b<sup>3<\/sup> to simplify the expression \\(\\frac{2}{\\sqrt[3]{x}+1}\\). Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-107.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 107\" width=\"542\" height=\"357\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-107.png 542w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-107-300x198.png 300w\" sizes=\"(max-width: 542px) 100vw, 542px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p>Graph the linear equation. Identify the x-intercept.<br \/>\nQuestion 108.<br \/>\ny = x &#8211; 4<br \/>\nAnswer:<\/p>\n<p>Question 109.<br \/>\ny = -2x + 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-109.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 109\" width=\"586\" height=\"350\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-109.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-109-300x179.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 110.<br \/>\ny = &#8211;\\(\\frac{1}{3}\\)x &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 111.<br \/>\ny = \\(\\frac{3}{2}\\)x + 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-111.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 111\" width=\"571\" height=\"345\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-111.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-111-300x181.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p><strong>Solve the equation. Check your solution.<\/strong><br \/>\nQuestion 112.<br \/>\n32 = 2<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 113.<br \/>\n27<sup>x<\/sup> = 3<sup>x &#8211; 6<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-113.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 113\" width=\"487\" height=\"327\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-113.png 487w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-113-300x201.png 300w\" sizes=\"(max-width: 487px) 100vw, 487px\" \/><\/p>\n<p>Question 114.<br \/>\n(\\(\\frac{1}{6}\\))<sup>2x<\/sup> = 216<sup>1 &#8211; x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 115.<br \/>\n625<sup>x<\/sup> = (\\(\\frac{1}{25}\\))<sup>x + 2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-115.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.1 a 115\" width=\"557\" height=\"533\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-115.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.1-a-115-300x287.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<h3><a id=\"Lesson_9.2_Solving_Quadratic_Equations_by_Graphing\"><\/a>Lesson 9.2 Solving Quadratic Equations by Graphing<\/h3>\n<p><strong>Essential Question<\/strong> How can you use a graph to solve a quadratic equation in one variable?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35284\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 1\" width=\"279\" height=\"245\" \/><br \/>\nBased on what you learned about the x-intercepts of a graph in Section 3.4, it follows that the x-intercept of the graph of the linear equation<br \/>\ny = ax + b 2 variables<br \/>\nis the same value as the solution of<br \/>\nax + b = 0. 1 variable<br \/>\nYou can use similar reasoning to solve quadratic equations.<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Solving a Quadratic Equation by Graphing<br \/>\nWork with a partner.<br \/>\na. Sketch the graph of y = x<sup>2<\/sup> &#8211; 2x.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35285\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 2\" width=\"247\" height=\"250\" \/><br \/>\nb. What is the definition of an x-intercept of a graph? How many x-intercepts does this graph have? What are they?<br \/>\nc. What is the definition of a solution of an equation in x? How many solutions does the equation x<sup>2<\/sup> &#8211; 2x = 0 have? What are they?<br \/>\nd. Explain how you can verify the solutions you found in part (c).<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Solving Quadratic Equations by Graphing<br \/>\nWork with a partner. Solve each equation by graphing.<br \/>\na. x<sup>2<\/sup> &#8211; 4 = 0<br \/>\nb. x<sup>2<\/sup> + 3x = 0<br \/>\nc. -x<sup>2<\/sup> + 2x + 1 = 0<br \/>\nd. x<sup>2<\/sup> &#8211; 2x + 1<br \/>\ne. x<sup>2<\/sup> &#8211; 3x + 5 = 0<br \/>\nf. -x<sup>2<\/sup> + 3x &#8211; 6 = 0<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you use a graph to solve a quadratic equation in one variable?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35286\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 3\" width=\"225\" height=\"182\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nAfter you find a solution graphically, how can you check your result algebraically? Check your solutions for parts (a)-(d) in Exploration 2 algebraically.<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nHow can you determine graphically that a quadratic equation has no solution?<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the equation by graphing. Check your solutions.<\/strong><br \/>\nQuestion 1.<br \/>\nx<sup>2<\/sup> &#8211; x &#8211; 2 = 0<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nx<sup>2<\/sup> + 7x = -10<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nx<sup>2<\/sup> + x = 12<br \/>\nAnswer:<\/p>\n<p><strong>Solve the equation by graphing.<\/strong><br \/>\nQuestion 4.<br \/>\nx<sup>2<\/sup> + 36 = 12x<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nx<sup>2<\/sup> + 4x = 0<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nx<sup>2<\/sup> + 10x = -25<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nx<sup>2<\/sup> = 3x &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nx<sup>2<\/sup> + 7x = -6<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n2x + 5 = -x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nGraph f(x) = x<sup>2<\/sup> + x &#8211; 6. Find the zeros of f.<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nGraph f(x) = -x<sup>2<\/sup> + 2x + 2. Approximate the zeros of f to the nearest tenth.<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nAfter how many seconds is the football 65 feet above the ground?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_by_Graphing_9.2_Exercises\"><\/a>Solving Quadratic Equations by Graphing 9.2 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat is a quadratic equation?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 1\" width=\"591\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-1.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-1-300x27.png 300w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich equation does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35287\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-4.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 4\" width=\"501\" height=\"43\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-4.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-4-300x26.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow can you use a graph to find the number of solutions of a quadratic equation?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 3\" width=\"575\" height=\"83\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-3.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-3-300x43.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow are solutions, roots, x-intercepts, and zeros related?<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u20138, use the graph to solve the equation.<\/strong><br \/>\nQuestion 5.<br \/>\n-x<sup>2<\/sup> + 2x + 3 = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35288\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 5\" width=\"155\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-41999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 5\" width=\"538\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-5.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-5-300x32.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 6.<br \/>\nx<sup>2<\/sup> &#8211; 6x + 8 = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35289\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-6.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 6\" width=\"150\" height=\"145\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nx<sup>2<\/sup> + 8x + 16 = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35290\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 7\" width=\"165\" height=\"153\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 7\" width=\"575\" height=\"56\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-7.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-7-300x29.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 8.<br \/>\n-x<sup>2<\/sup> &#8211; 4x &#8211; 6 = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35291\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-8.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 8\" width=\"143\" height=\"150\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 9\u201312, write the equation in standard form.<\/strong><br \/>\nQuestion 9.<br \/>\n4x<sup>2<\/sup> = 12<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 9\" width=\"545\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-9.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-9-300x77.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 10.<br \/>\n-x<sup>2<\/sup> = 15<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n2x &#8211; x<sup>2<\/sup> = 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 11\" width=\"440\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-11.png 440w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-11-300x110.png 300w\" sizes=\"(max-width: 440px) 100vw, 440px\" \/><\/p>\n<p>Question 12.<br \/>\n5 + x = 3x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 13\u201324, solve the equation by graphing.<\/strong><br \/>\nQuestion 13.<br \/>\nx<sup>2<\/sup> &#8211; 5x = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 13\" width=\"557\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-13.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-13-300x183.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 14.<br \/>\nx<sup>2<\/sup> &#8211; 4x + 4 = 0<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nx<sup>2<\/sup> &#8211; 2x + 5 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 15\" width=\"535\" height=\"336\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-15.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-15-300x188.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Question 16.<br \/>\nx<sup>2<\/sup> &#8211; 6x &#8211; 7 = 0<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nx<sup>2<\/sup> &#8211; 6x = 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 17\" width=\"538\" height=\"455\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-17.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-17-300x254.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 18.<br \/>\n-x<sup>2<\/sup> = 8x + 20<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nx<sup>2<\/sup> = -1 &#8211; 2x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 19\" width=\"572\" height=\"445\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-19.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-19-300x233.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 20.<br \/>\nx<sup>2<\/sup> = -x &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n4x &#8211; 12 = -x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 21\" width=\"553\" height=\"444\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-21.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-21-300x241.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 22.<br \/>\n5x &#8211; 6 = x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nx<sup>2<\/sup> &#8211; 2 = -x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 23\" width=\"559\" height=\"439\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-23.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-23-300x236.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 24.<br \/>\n16 + x<sup>2<\/sup> = -8x<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving x<sup>2<\/sup> + 3x = 18 by graphing.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35292\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 9\" width=\"329\" height=\"233\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-9.png 329w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-9-300x212.png 300w\" sizes=\"(max-width: 329px) 100vw, 329px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 25\" width=\"512\" height=\"483\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-25.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-25-300x283.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 26.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving x<sup>2<\/sup> + 6x + 9 = 0 by graphing.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35293\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-10.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 10\" width=\"314\" height=\"227\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-10.png 314w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-10-300x217.png 300w\" sizes=\"(max-width: 314px) 100vw, 314px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe height y (in yards) of a flop shot in golf can be modeled by y = -x<sup>2<\/sup> + 5x, where x is the horizontal distance (in yards).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35294\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 11\" width=\"176\" height=\"115\" \/><br \/>\na. Interpret the x-intercepts of the graph of the equation.<br \/>\nb. How far away does the golf ball land?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 27\" width=\"548\" height=\"473\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-27.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-27-300x259.png 300w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe height h (in feet) of an underhand volleyball serve can be modeled by h = -16t<sup>2<\/sup> + 30t + 4, where t is the time (in seconds).<br \/>\na. Do both t-intercepts of the graph of the function have meaning in this situation? Explain.<br \/>\nb. No one receives the serve. After how many seconds does the volleyball hit the ground?<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 29\u201336, solve the equation by using Method 2 from Example 3.<\/strong><br \/>\nQuestion 29.<br \/>\nx<sup>2<\/sup> = 10 &#8211; 3x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 29\" width=\"581\" height=\"443\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-29.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-29-300x229.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 30.<br \/>\n2x &#8211; 3 = x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n5x &#8211; 7 = x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 31\" width=\"580\" height=\"412\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-31.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-31-300x213.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 32.<br \/>\nx<sup>2<\/sup> = 6x &#8211; 5<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\nx<sup>2<\/sup> + 12x = -20<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 33\" width=\"552\" height=\"425\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-33.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-33-300x231.png 300w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><\/p>\n<p>Question 34.<br \/>\nx<sup>2<\/sup> + 8x = 9<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n-x<sup>2<\/sup> &#8211; 5 = -2x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-35.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 35\" width=\"453\" height=\"408\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-35.png 453w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-35-300x270.png 300w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/p>\n<p>Question 36.<br \/>\n-x<sup>2<\/sup> &#8211; 4 = -4x<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 37\u201342, find the zero(s) of f.<\/strong><br \/>\nQuestion 37.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35295\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-12.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 12\" width=\"148\" height=\"152\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 37\" width=\"387\" height=\"589\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-37.png 387w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-37-197x300.png 197w\" sizes=\"(max-width: 387px) 100vw, 387px\" \/><\/p>\n<p>Question 38.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35296\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 13\" width=\"185\" height=\"155\" \/><br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35297\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-14.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 14\" width=\"196\" height=\"150\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 39\" width=\"452\" height=\"482\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-39.png 452w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-39-281x300.png 281w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/p>\n<p>Question 40.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35298\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 15\" width=\"193\" height=\"154\" \/><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35299\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-16.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 16\" width=\"190\" height=\"158\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-41.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 41.1\" width=\"465\" height=\"445\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-41.1.png 465w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-41.1-300x287.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-41.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 41.2\" width=\"475\" height=\"454\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-41.2.png 475w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-41.2-300x287.png 300w\" sizes=\"(max-width: 475px) 100vw, 475px\" \/><\/p>\n<p>Question 42<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35300\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 17\" width=\"188\" height=\"169\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 43\u201346, approximate the zeros of f to the nearest tenth.<\/strong><br \/>\nQuestion 43.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35301\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-18.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 18\" width=\"146\" height=\"156\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 43\" width=\"572\" height=\"591\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-43.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-43-290x300.png 290w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 44.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35302\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 19\" width=\"148\" height=\"165\" \/><br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35303\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-20.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 20\" width=\"149\" height=\"159\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 45\" width=\"549\" height=\"598\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-45.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-45-275x300.png 275w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 46.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35304\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 21\" width=\"156\" height=\"156\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-21.png 156w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-21-150x150.png 150w\" sizes=\"(max-width: 156px) 100vw, 156px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 47\u201352, graph the function. Approximate the zeros of the function to the nearest tenth, if necessary.<\/strong><br \/>\nQuestion 47.<br \/>\nf(x) = x<sup>2<\/sup> + 6x + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-47.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 47.1\" width=\"480\" height=\"470\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-47.1.png 480w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-47.1-300x294.png 300w\" sizes=\"(max-width: 480px) 100vw, 480px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-47.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 47.2\" width=\"581\" height=\"438\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-47.2.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-47.2-300x226.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 48.<br \/>\nf(x) = x<sup>2<\/sup> &#8211; 3x + 2<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\ny = -x<sup>2<\/sup> + 4x &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-49.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 49.1\" width=\"544\" height=\"550\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-49.1.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-49.1-297x300.png 297w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-49.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 49.2\" width=\"567\" height=\"319\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-49.2.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-49.2-300x169.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 50.<br \/>\ny = -x<sup>2<\/sup> + 9x &#8211; 6<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\nf(x) = \\(\\frac{1}{2}\\)x<sup>2<\/sup> + 2x &#8211; 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-51.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 51.1\" width=\"503\" height=\"563\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-51.1.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-51.1-268x300.png 268w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42026\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-51.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 51.2\" width=\"581\" height=\"309\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-51.2.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-51.2-300x160.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 52.<br \/>\nf(x) = -3x<sup>2<\/sup> + 4x + 3<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nAt a Civil War reenactment, a cannonball is fired into the air with an initial vertical velocity of 128 feet per second. The release point is 6 feet above the ground. The function h = -16t<sup>2<\/sup> + 128t + 6 represents the height h (in feet) of the cannonball after t seconds.<br \/>\na. Find the height of the cannonball each second after it is fired.<br \/>\nb. Use the results of part (a) to estimate when the height of the cannonball is 150 feet.<br \/>\nc. Using a graph, after how many seconds is the cannonball 150 feet above the ground?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35305\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-22.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 22\" width=\"159\" height=\"137\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42027\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-53.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 53.1\" width=\"578\" height=\"533\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-53.1.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-53.1-300x277.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-53.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 53.2\" width=\"565\" height=\"232\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-53.2.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-53.2-300x123.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou throw a softball straight up into the air with an initial vertical velocity of 40 feet per second. The release point is 5 feet above the ground. The function h = -16t<sup>2<\/sup> + 40t + 5 represents the height h (in feet) of the softball after t seconds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35306\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 23\" width=\"131\" height=\"134\" \/><br \/>\na. Find the height of the softball each second after it is released.<br \/>\nb. Use the results of part (a) to estimate when the height of the softball is 15 feet.<br \/>\nc. Using a graph, after how many seconds is the softball 15 feet above the ground?<br \/>\nAnswer:<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong> In Exercises 55 and 56, use the given surface area S of the cylinder to find the radius r to the nearest tenth.<br \/>\nQuestion 55.<br \/>\nS = 225 ft<sup>2<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35307\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-24.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 24\" width=\"137\" height=\"118\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-55.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 55\" width=\"573\" height=\"453\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-55.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-55-300x237.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 56.<br \/>\nS = 750 m<sup>2<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35308\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 25\" width=\"135\" height=\"123\" \/><br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to approximate zeros of a function when the zeros are not integers.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42030\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-57.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 57\" width=\"587\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-57.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-57-300x85.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nConsider the graph shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35309\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-26.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 26\" width=\"175\" height=\"159\" \/><br \/>\na. How many solutions does the quadratic equation x<sup>2<\/sup> = -3x + 4 have? Explain.<br \/>\nb. Without graphing, describe what you know about the graph of y = x<sup>2<\/sup> + 3x &#8211; 4.<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nExample 3 shows two methods for solving a quadratic equation. Which method do you prefer? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42031\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-59.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 59\" width=\"586\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-59.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-59-300x31.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nHow many different parabolas have -2 and 2 as x-intercepts? Sketch examples of parabolas that have these two x-intercepts.<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nTo keep water off a road, the surface of the road is shaped like a parabola. A cross section of the road is shown in the diagram. The surface of the road can be modeled by y = -0.0017x<sup>2<\/sup> + 0.041x, where x and y are measured in feet. Find the width of the road to the nearest tenth of a foot.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35310\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-27.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 27.1\" width=\"255\" height=\"100\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-61.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 61\" width=\"557\" height=\"269\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-61.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-61-300x145.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nA stream of water from a fire hose can be modeled by y = -0.003x<sup>2<\/sup> + 0.58x + 3,where x and y are measured in feet. A firefighter is standing 57 feet from a building and is holding the hose 3 feet above the ground. The bottom of a window of the building is 26 feet above the ground. Your friend claims the stream of water will pass through the window. Is your friend correct? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>REASONING<\/strong> In Exercises 63\u201365, determine whether the statement is always, sometimes, or never true. Justify your answer.<br \/>\nQuestion 63.<br \/>\nThe graph of y = ax<sup>2<\/sup> + c has two x-intercepts when a is negative.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-63.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 63\" width=\"583\" height=\"145\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-63.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-63-300x75.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 64.<br \/>\nThe graph of y = ax<sup>2<\/sup> + c has no x-intercepts when a and c have the same sign.<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\nThe graph of y = ax<sup>2<\/sup> + bx + c has more than two x-intercepts when a \u2260 0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-65.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 65\" width=\"528\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-65.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-65-300x49.png 300w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p>Determine whether the table represents an exponential growth function, an exponential decay function, or neither. Explain.<br \/>\nQuestion 66.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35311\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 27\" width=\"213\" height=\"74\" \/><br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35312\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-28.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 28\" width=\"213\" height=\"72\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-67.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations 9.2 a 67\" width=\"550\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-67.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-9.2-a-67-300x141.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<h3><a id=\"Lesson_9.3_Solving_Quadratic_Equations_Using_Square_Roots\"><\/a>Lesson 9.3 Solving Quadratic Equations Using Square Roots<\/h3>\n<p><strong>Essential Question<\/strong> How can you determine the number of solutions of a quadratic equation of the form ax<sup>2<\/sup> + c = 0?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>The Number of Solutions of ax<sup>2<\/sup> + c = 0<br \/>\nWork with a partner. Solve each equation by graphing. Explain how the number of solutions of ax<sup>2<\/sup> + c = 0 relates to the graph of y = ax<sup>2<\/sup> + c.<br \/>\na. x<sup>2<\/sup> &#8211; 4 = 0<br \/>\nb. 2x<sup>2<\/sup> + 5 = 0<br \/>\nc. x<sup>2<\/sup> = 0<br \/>\nd. x<sup>2<\/sup> &#8211; 5 = 0<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Estimating Solutions<br \/>\nWork with a partner. Complete each table. Use the completed tables to estimate the solutions of x<sup>2<\/sup> &#8211; 5 = 0. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35313\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 1\" width=\"448\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-1.png 448w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-1-300x131.png 300w\" sizes=\"(max-width: 448px) 100vw, 448px\" \/><\/p>\n<p><strong>EXPLORATION 3<\/strong><\/p>\n<p>Using Technology to Estimate Solutions<br \/>\nWork with a partner. Two equations are equivalent when they have the same solutions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35314\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 2\" width=\"221\" height=\"208\" \/><br \/>\na. Are the equations x<sup>2<\/sup> &#8211; 5 = 0 and x<sup>2<\/sup> = 5 equivalent? Explain your reasoning.<br \/>\nb. Use the square root key on a calculator to estimate the solutions of x<sup>2<\/sup> &#8211; 5 = 0. Describe the accuracy of your estimates in Exploration 2.<br \/>\nc. Write the exact solutions of x<sup>2<\/sup> &#8211; 5 = 0.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you determine the number of solutions of a quadratic equation of the form ax<sup>2<\/sup> + c = 0?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nWrite the exact solutions of each equation. Then use a calculator to estimate the solutions.<br \/>\na. x<sup>2<\/sup> &#8211; 2 = 0<br \/>\nb. 3x<sup>2<\/sup> &#8211; 18 = 0<br \/>\nc. x<sup>2<\/sup> &#8211; 8<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the equation using square roots.<\/strong><br \/>\nQuestion 1.<br \/>\n-3x<sup>2<\/sup> = -75<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nx<sup>2<\/sup> + 12 = 10<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n4x<sup>2<\/sup> &#8211; 15 = -15<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n(x + 7)<sup>2<\/sup> = 0<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n4(x &#8211; 3)<sup>2<\/sup> = 9<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n(2x + 1)<sup>2<\/sup> = 36<br \/>\nAnswer:<\/p>\n<p><strong>Solve the equation using square roots. Round your solutions to the nearest hundredth.<\/strong><br \/>\nQuestion 7.<br \/>\nx<sup>2<\/sup> + 8 = 19<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n5x<sup>2<\/sup> &#8211; 2 = 0<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n3x<sup>2<\/sup> &#8211; 30 = 4<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35315\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 3\" width=\"183\" height=\"125\" \/><br \/>\nQuestion 10.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nIn Example 4, the volume of the tank is 315 cubic feet. Find the length and width of the tank.<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nThe surface area S of a sphere with radius r is given by the formula S = 4\u03c0r<sup>2<\/sup>. Solve the formula for r. Then find the radius of a globe with a surface area of 804 square inches.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Using_Square_Roots_9.3_Exercises\"><\/a>Solving Quadratic Equations Using Square Roots 9.3 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe equation x<sup>2<\/sup> = d has ____ real solutions when d &gt; 0.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 1\" width=\"525\" height=\"37\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-1.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-1-300x21.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nWhich is different? Find \u201cboth\u201d answers<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35316\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-4.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 4\" width=\"559\" height=\"96\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-4.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-4-300x52.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20138, determine the number of real solutions of the equation. Then solve the equation using square roots.<\/strong><br \/>\nQuestion 3.<br \/>\nx<sup>2<\/sup> = 25<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 3\" width=\"481\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-3.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-3-300x105.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>Question 4.<br \/>\nx<sup>2<\/sup> = -36<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nx<sup>2<\/sup> = -21<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42039\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 5\" width=\"503\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-5.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-5-300x18.png 300w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<p>Question 6.<br \/>\nx<sup>2<\/sup> = 400<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nx<sup>2<\/sup> = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42040\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 7\" width=\"404\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-7.png 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-7-300x128.png 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><\/p>\n<p>Question 8.<br \/>\nx<sup>2<\/sup> = 169<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 9\u201318, solve the equation using square roots.<\/strong><br \/>\nQuestion 9.<br \/>\nx<sup>2<\/sup> &#8211; 16 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42041\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-9.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 9\" width=\"363\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-9.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-9-300x170.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<p>Question 10.<br \/>\nx<sup>2<\/sup> + 6 = 0<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n3x<sup>2<\/sup> + 12 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42042\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-11.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 11\" width=\"516\" height=\"257\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-11.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-11-300x149.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<p>Question 12.<br \/>\nx<sup>2<\/sup> &#8211; 55 = 26<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n2x<sup>2<\/sup> &#8211; 98 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-13.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 13\" width=\"343\" height=\"295\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-13.png 343w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-13-300x258.png 300w\" sizes=\"(max-width: 343px) 100vw, 343px\" \/><\/p>\n<p>Question 14.<br \/>\n-x<sup>2<\/sup> + 9 = 9<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n-3x<sup>2<\/sup> &#8211; 5 = -5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-15.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 15\" width=\"263\" height=\"313\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-15.png 263w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-15-252x300.png 252w\" sizes=\"(max-width: 263px) 100vw, 263px\" \/><\/p>\n<p>Question 16.<br \/>\n4x<sup>2<\/sup> &#8211; 371 = 29<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n4x<sup>2<\/sup> + 10 = 11<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-17.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 17\" width=\"342\" height=\"408\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-17.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-17-251x300.png 251w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/p>\n<p>Question 18.<br \/>\n9x<sup>2<\/sup> &#8211; 35 = 14<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 19\u201324, solve the equation using square roots.<\/strong><br \/>\nQuestion 19.<br \/>\n(x + 3)<sup>2<\/sup> = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-19.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 19\" width=\"273\" height=\"221\" \/><\/p>\n<p>Question 20.<br \/>\n(x &#8211; 1)<sup>2<\/sup> = 4<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n(2x &#8211; 1)<sup>2<\/sup> = 81<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-21.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 21\" width=\"416\" height=\"475\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-21.png 416w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-21-263x300.png 263w\" sizes=\"(max-width: 416px) 100vw, 416px\" \/><\/p>\n<p>Question 22.<br \/>\n(4x + 5)<sup>2<\/sup> = 9<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n9(x + 1)<sup>2<\/sup> = 16<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-23.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 23\" width=\"576\" height=\"415\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-23.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-23-300x216.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 24.<br \/>\n4(x &#8211; 2)<sup>2<\/sup> = 25<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 25\u201330, solve the equation using square roots. Round your solutions to the nearest hundredth.<\/strong><br \/>\nQuestion 25.<br \/>\nx<sup>2<\/sup> + 6 = 13<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-25.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 25\" width=\"408\" height=\"328\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-25.png 408w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-25-300x241.png 300w\" sizes=\"(max-width: 408px) 100vw, 408px\" \/><\/p>\n<p>Question 26.<br \/>\nx<sup>2<\/sup> + 11 = 24<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n2x<sup>2<\/sup> &#8211; 9 = 11<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-27.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 27\" width=\"400\" height=\"315\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-27.png 400w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-27-300x236.png 300w\" sizes=\"(max-width: 400px) 100vw, 400px\" \/><\/p>\n<p>Question 28.<br \/>\n5x<sup>2<\/sup> + 2 = 6<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n-21 = 15 &#8211; 2x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-29.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 29\" width=\"401\" height=\"399\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-29.png 401w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-29-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-29-150x150.png 150w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><\/p>\n<p>Question 30.<br \/>\n2 = 4x<sup>2<\/sup> &#8211; 5<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving the equation 2x<sup>2<\/sup> &#8211; 33 = 39 using square roots.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35317\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 5\" width=\"323\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-5.png 323w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-5-300x131.png 300w\" sizes=\"(max-width: 323px) 100vw, 323px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-31.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 31\" width=\"556\" height=\"329\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-31.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-31-300x178.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nAn in-ground pond has the shape of a rectangular prism. The pond has a depth of 24 inches and a volume of 72,000 cubic inches. The length of the pond is two times its width. Find the length and width of the pond.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35318\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-6.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 6\" width=\"274\" height=\"171\" \/><br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA person sitting in the top row of the bleachers at a sporting event drops a pair of sunglasses from a height of 24 feet. The function h = -16x<sup>2<\/sup> + 24 represents the height h (in feet) of the sunglasses after x seconds. How long does it take the sunglasses to hit the ground?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-33.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 33\" width=\"530\" height=\"592\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-33.png 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-33-269x300.png 269w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that the solution of the equation x<sup>2<\/sup> + 4 = 0 is x = 0. Your cousin says that the equation has no real solutions. Who is correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe design of a square rug for your living room is shown. You want the area of the inner square to be 25% of the total area of the rug. Find the side length x of the inner square.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35319\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 7\" width=\"169\" height=\"174\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-35.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 35\" width=\"571\" height=\"229\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-35.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-35-300x120.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe area A of a circle with radius r is given by the formula A = \u03c0r<sup>2<\/sup>.<br \/>\na. Solve the formula for r.<br \/>\nb. Use the formula from part (a) to find the radius of each circle.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35320\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-8.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 8\" width=\"309\" height=\"122\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-8.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-8-300x118.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\nc. Explain why it is beneficial to solve the formula for r before finding the radius.<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow can you approximate the roots of a quadratic equation when the roots are not integers?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-37.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 37\" width=\"514\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-37.png 514w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-37-300x33.png 300w\" sizes=\"(max-width: 514px) 100vw, 514px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>WRITING<\/strong><br \/>\nGiven the equation ax<sup>2<\/sup> + c = 0, describe the values of a and c so the equation has the following number of solutions.<br \/>\na. two real solutions<br \/>\nb. one real solution<br \/>\nc. no real solutions<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>REASONING<\/strong><br \/>\nWithout graphing, where do the graphs of y = x<sup>2<\/sup> and y = 9 intersect? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-39.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 39\" width=\"499\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-39.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-39-300x51.png 300w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph represents the function f(x) = (x &#8211; 1)<sup>2<\/sup>. How many solutions does the equation (x &#8211; 1)<sup>2<\/sup> = 0 have? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35321\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-9.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 9\" width=\"176\" height=\"171\" \/><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>REASONING<\/strong><br \/>\nSolve x<sup>2<\/sup> = 1.44 without using a calculator. Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-41.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 41\" width=\"501\" height=\"195\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-41.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-41-300x117.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nThe quadratic equation ax<sup>2<\/sup> + bx + c = 0can be rewritten in the following form. \\(\\left(x+\\frac{b}{2 a}\\right)^{2}=\\frac{b^{2}-4 a c}{4 a^{2}}\\) Use this form to write the solutions of the equation.<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>REASONING<\/strong><br \/>\nAn equation of the graph shown is y = \\(\\frac{1}{2}\\)(x &#8211; 2)<sup>2<\/sup> + 1. Two points on the parabola have y-coordinates of 9. Find the x-coordinates of these points.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35322\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-10.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 10\" width=\"161\" height=\"123\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-43.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 43\" width=\"559\" height=\"381\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-43.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-43-300x204.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nSolve each equation without graphing.<br \/>\na. x<sup>2<\/sup> &#8211; 12x + 36 = 64<br \/>\nb. x<sup>2<\/sup> + 14x + 49 = 16<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Factor the polynomial.<\/strong><br \/>\nQuestion 45.<br \/>\nx<sup>2<\/sup> + 8x + 16<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-45.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 45\" width=\"337\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-45.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-45-300x58.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><\/p>\n<p>Question 46.<br \/>\nx<sup>2<\/sup> &#8211; 4x + 4<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\nx<sup>2<\/sup> &#8211; 14x + 49<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-47.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 47\" width=\"334\" height=\"67\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-47.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-47-300x60.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/p>\n<p>Question 48.<br \/>\nx<sup>2<\/sup> + 18x + 81<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\nx<sup>2<\/sup> + 12x + 36<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-49.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 a 49\" width=\"342\" height=\"70\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-49.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-a-49-300x61.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/p>\n<p>Question 50.<br \/>\nx<sup>2<\/sup> &#8211; 22x + 121<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Study_Skills:_Keeping_a_Positive_Attitude\"><\/a>Solving Quadratic Equations Study Skills: Keeping a Positive Attitude<\/h3>\n<p><strong>9.1\u20139.3 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35323\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-11.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 11\" width=\"510\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-11.png 510w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-11-300x51.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35324\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-12.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 12\" width=\"621\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-12.png 621w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-12-300x107.png 300w\" sizes=\"(max-width: 621px) 100vw, 621px\" \/><\/p>\n<p><strong>Mathematical Practices<\/strong><\/p>\n<p>Question 1.<br \/>\nFor each part of Exercise 100 on page 488 that is sometimes true, list all examples and counterexamples from the table that represent the sum or product being described.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nWhich Examples can you use to help you solve Exercise 54 on page 496?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nDescribe how solving a simpler equation can help you solve the equation in Exercise 41 on page 502.<br \/>\nAnswer:<\/p>\n<p><strong>Study Skills: Keeping a Positive Attitude<\/strong><\/p>\n<p>Do you ever feel frustrated or overwhelmed by math? You\u2019re not alone. Just take a deep breath and assess the situation. Try to find a productive study environment, review your notes and the examples in the textbook, and ask your teacher or friends for help.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35325\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-13.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations 9.3 13\" width=\"363\" height=\"272\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-13.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-9.3-13-300x225.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/p>\n<h3><a id=\"Solving_Quadratic_Equations_9.1_\u2013_9.3_Quiz\"><\/a>Solving Quadratic Equations 9.1 \u2013 9.3 Quiz<\/h3>\n<p><strong>Simplify the expression.<\/strong><br \/>\nQuestion 1.<br \/>\n\\(\\sqrt{112 x^{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\\(\\sqrt{\\frac{18}{81}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt[3]{-625}\\)<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{12}{\\sqrt{32}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n\\(\\frac{4}{\\sqrt{11}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n\\(\\sqrt{\\frac{144}{13}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n\\(\\sqrt[3]{\\frac{54 x^{4}}{343 y^{6}}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt{\\frac{4 x^{2}}{28 y^{4} z^{5}}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{6}{5+\\sqrt{3}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n2\\(\\sqrt{5}\\) + 7\\(\\sqrt{10}\\) &#8211; 3\\(\\sqrt{20}\\)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n\\(\\frac{10}{\\sqrt{8}-\\sqrt{10}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n\\(\\sqrt{6}\\)(7\\(\\sqrt{12}\\) &#8211; 4\\(\\sqrt{3}\\))<br \/>\nAnswer:<\/p>\n<p><strong>Use the graph to solve the equation.<\/strong><br \/>\nQuestion 13.<br \/>\nx<sup>2<\/sup> &#8211; 2x &#8211; 3 = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35326\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-q-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations q 1\" width=\"199\" height=\"195\" \/><br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nx<sup>2<\/sup> &#8211; 2x + 3 = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35327\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-q-2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations q 2\" width=\"185\" height=\"194\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nx<sup>2<\/sup> + 10x + 25 = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35328\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-q-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations q 3\" width=\"208\" height=\"198\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Solve the equation by graphing.<\/strong><br \/>\nQuestion 16.<br \/>\nx<sup>2<\/sup> + 9x + 14 = 0<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nx<sup>2<\/sup> &#8211; 7x = 8<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\nx + 4 = -x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>Solve the equation using square roots.<\/strong><br \/>\nQuestion 19.<br \/>\n4x<sup>2<\/sup> = 64<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\n-3x<sup>2<\/sup> + 6 = 10<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n(x &#8211; 8)<sup>2<\/sup> = 1<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\nExplain how to determine the number of real solutions of x<sup>2<\/sup> = 100 without solving.<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nThe length of a rectangular prism is four times its width. The volume of the prism is 380 cubic meters. Find the length and width of the prism.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35329\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-q-4.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations q 4\" width=\"264\" height=\"100\" \/><br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\nYou cast a fishing lure into the water from a height of 4 feet above the water. The height h (in feet) of the fishing lure after t seconds can be modeled by the equation h = -16t<sup>2<\/sup> + 24t + 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35330\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-q-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations q 5\" width=\"298\" height=\"189\" \/><br \/>\na. After how many seconds does the fishing lure reach a height of 12 feet?<br \/>\nb. After how many seconds does the fishing lure hit the water?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_9.4_Solving_Quadratic_Equations_by_Completing_the_Square\"><\/a>Lesson 9.4 Solving Quadratic Equations by Completing the Square<\/h3>\n<p><strong>Essential Question<\/strong> How can you use \u201ccompleting the square\u201d to solve a quadratic equation?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Solving by Completing the Square<br \/>\nWork with a partner.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35331\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 1\" width=\"294\" height=\"453\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-1.png 294w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-1-195x300.png 195w\" sizes=\"(max-width: 294px) 100vw, 294px\" \/><br \/>\na. Write the equation modeled by the algebra tiles. This is the equation to be solved.<br \/>\nb. Four algebra tiles are added to the left side to \u201ccomplete the square.\u201d Why are four algebra tiles also added to the right side?<br \/>\nc. Use algebra tiles to label the dimensions of the square on the left side and simplify on the right side.<br \/>\nd. Write the equation modeled by the algebra tiles so that the left side is the square of a binomial. Solve the equation using square roots.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Solving by Completing the Square<br \/>\nWork with a partner.<br \/>\na. Write the equation modeled by the algebra tiles.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35332\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 2\" width=\"501\" height=\"291\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-2.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-2-300x174.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><br \/>\nb. Use algebra tiles to \u201ccomplete the square.\u201d<br \/>\nc. Write the solutions of the equation.<br \/>\nd. Check each solution in the original equation.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you use \u201ccompleting the square\u201d to solve a quadratic equation?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nSolve each quadratic equation by completing the square.<br \/>\na. x<sup>2<\/sup> &#8211; 2x = 1<br \/>\nb. x<sup>2<\/sup> &#8211; 4x = -1<br \/>\nc. x<sup>2<\/sup> + 4x = -3<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Complete the square for the expression. Then factor the trinomial.<\/strong><br \/>\nQuestion 1.<br \/>\nx<sup>2<\/sup> + 10x<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nx<sup>2<\/sup> &#8211; 4x<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nx<sup>2<\/sup> + 7x<br \/>\nAnswer:<\/p>\n<p><strong>Solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.<\/strong><br \/>\nQuestion 4.<br \/>\nx<sup>2<\/sup> &#8211; 2x = 3<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nm<sup>2<\/sup> + 12m = -8<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n3g<sup>2<\/sup> &#8211; 24g + 27 = 0<br \/>\nAnswer:<\/p>\n<p><strong>Determine whether the quadratic function has a maximum or minimum value. Then find the value.<\/strong><br \/>\nQuestion 7.<br \/>\ny = -x<sup>2<\/sup> &#8211; 4x + 4<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\ny = x<sup>2<\/sup> + 12x + 40<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ny = x<sup>2<\/sup> &#8211; 2x &#8211; 2<br \/>\nAnswer:<\/p>\n<p><strong>Determine whether the function could be represented by the graph in Example 6. Explain.<\/strong><br \/>\nQuestion 10.<br \/>\nh(x) = (x &#8211; 8)<sup>2<\/sup> + 10<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nn(x) = -2(x &#8211; 5)(x &#8211; 20)<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nRepeat Example 7 when the function is y = -16x<sup>2<\/sup> + 128x.<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nYou want the chalkboard to cover 4 square feet. Find the width of the border to the nearest inch.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_by_Completing_the_Square_9.4_Exercises\"><\/a>Solving Quadratic Equations by Completing the Square 9.4 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>COMPLETE THE SENTENCE<\/strong><br \/>\nThe process of adding a constant c to the expression x<sup>2<\/sup> + bx so that x<sup>2<\/sup> + bx + c is a perfect square trinomial is called ________________.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 1\" width=\"540\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-1.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-1-300x48.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nExplain how to complete the square for an expression of the form x<sup>2<\/sup> + bx.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>WRITING<\/strong><br \/>\nIs it more convenient to complete the square for x<sup>2<\/sup> + bx when b is odd or when b is even? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 3\" width=\"546\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-3.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-3-300x48.png 300w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe how you can use the process of completing the square to find the maximum or minimum value of a quadratic function.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u201310, find the value of c that completes the square.<\/strong><br \/>\nQuestion 5.<br \/>\nx<sup>2<\/sup> &#8211; 8x + c<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42064\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-5.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 5\" width=\"257\" height=\"87\" \/><\/p>\n<p>Question 6.<br \/>\nx<sup>2<\/sup> &#8211; 2x + c<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nx<sup>2<\/sup> + 4x + c<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-7.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 7\" width=\"186\" height=\"87\" \/><\/p>\n<p>Question 8.<br \/>\nx<sup>2<\/sup> + 12x + c<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nx<sup>2<\/sup> &#8211; 15x + c<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-9.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 9\" width=\"182\" height=\"87\" \/><\/p>\n<p>Question 10.<br \/>\nx<sup>2<\/sup> + 9x + c<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 11\u201316, complete the square for the expression. Then factor the trinomial.<\/strong><br \/>\nQuestion 11.<br \/>\nx<sup>2<\/sup> &#8211; 10x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-11.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 11\" width=\"307\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-11.png 307w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-11-300x186.png 300w\" sizes=\"(max-width: 307px) 100vw, 307px\" \/><\/p>\n<p>Question 12.<br \/>\nx<sup>2<\/sup> &#8211; 40x<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nx<sup>2<\/sup> + 16x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42068\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-13.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 13\" width=\"293\" height=\"194\" \/><\/p>\n<p>Question 14.<br \/>\nx<sup>2<\/sup> + 22x<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nx<sup>2<\/sup> + 5x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-15.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 15\" width=\"304\" height=\"265\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-15.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-15-300x262.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><\/p>\n<p>Question 16.<br \/>\nx<sup>2<\/sup> &#8211; 3x<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 17\u201322, solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.<\/strong><br \/>\nQuestion 17.<br \/>\nx<sup>2<\/sup> + 14x = 15<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-17.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 17\" width=\"555\" height=\"307\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-17.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-17-300x166.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 18.<br \/>\nx<sup>2<\/sup> &#8211; 6x = 16<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nx<sup>2<\/sup> &#8211; 4x = -2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-19.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 19\" width=\"402\" height=\"335\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-19.png 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-19-300x250.png 300w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p>Question 20.<br \/>\nx<sup>2<\/sup> + 2x = 5<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nx<sup>2<\/sup> &#8211; 5x = 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-21.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 21\" width=\"402\" height=\"608\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-21.png 402w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-21-198x300.png 198w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<p>Question 22.<br \/>\nx<sup>2<\/sup> + 11x = -10<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe area of the patio is 216 square feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35333\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 3\" width=\"151\" height=\"135\" \/><br \/>\na. Write an equation that represents the area of the patio.<br \/>\nb. Find the dimensions of the patio by completing the square.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-23.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 23\" width=\"547\" height=\"689\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-23.png 547w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-23-238x300.png 238w\" sizes=\"(max-width: 547px) 100vw, 547px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nSome sand art contains sand and water sealed in a glass case, similar to the one shown. When the art is turned upside down, the sand and water fall to create a new picture. The glass case has a depth of 1 centimeter and a volume of 768 cubic centimeters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35334\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-4.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 4\" width=\"280\" height=\"135\" \/><br \/>\na. Write an equation that represents the volume of the glass case.<br \/>\nb. Find the dimensions of the glass case by completing the square.<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 25\u201332, solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.<\/strong><br \/>\nQuestion 25.<br \/>\nx<sup>2<\/sup> &#8211; 8x + 15 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-25.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 25\" width=\"506\" height=\"379\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-25.png 506w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-25-300x225.png 300w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><\/p>\n<p>Question 26.<br \/>\nx<sup>2<\/sup> + 4x &#8211; 21 = 0<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n2x<sup>2<\/sup> + 20x + 44 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-27.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 27\" width=\"435\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-27.png 435w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-27-263x300.png 263w\" sizes=\"(max-width: 435px) 100vw, 435px\" \/><\/p>\n<p>Question 28.<br \/>\n3x<sup>2<\/sup> &#8211; 18x + 12 = 0<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n-3x<sup>2<\/sup> &#8211; 24x + 17 = -40<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-29.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 29\" width=\"422\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-29.png 422w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-29-255x300.png 255w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><\/p>\n<p>Question 30.<br \/>\n-5x<sup>2<\/sup> &#8211; 20x + 35 = 30<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n2x<sup>2<\/sup> &#8211; 14x + 10 = 26<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-31.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 31\" width=\"418\" height=\"744\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-31.png 418w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-31-169x300.png 169w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p>Question 32.<br \/>\n4x<sup>2<\/sup> + 12x &#8211; 15 = 5<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving x<sup>2<\/sup> + 8x = 10 by completing the square.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35335\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-5.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 5\" width=\"316\" height=\"127\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-5.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-5-300x121.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-33.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 33\" width=\"516\" height=\"399\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-33.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-33-300x232.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in the first two steps of solving 2x<sup>2<\/sup> &#8211; 2x &#8211; 4 = 0 by completing the square.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35336\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-6.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 6\" width=\"271\" height=\"97\" \/><br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>NUMBER SENSE<\/strong><br \/>\nFind all values of b for which x<sup>2<\/sup> + bx + 25 is a perfect square trinomial. Explain how you found your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-35.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 35\" width=\"545\" height=\"444\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-35.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-35-300x244.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou are completing the square to solve 3x<sup>2<\/sup> + 6x = 12. What is the first step?<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 37\u201340, write the function in vertex form by\ue04acompleting the square. Then match the function with its graph.<\/strong><br \/>\nQuestion 37.<br \/>\ny = x<sup>2<\/sup> + 6x + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-37.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 37\" width=\"572\" height=\"340\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-37.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-37-300x178.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 38.<br \/>\ny = -x<sup>2<\/sup> + 8x &#8211; 12<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\ny = -x<sup>2<\/sup> &#8211; 4x &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42081\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-39.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 39\" width=\"556\" height=\"376\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-39.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-39-300x203.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 40.<br \/>\ny = x<sup>2<\/sup> &#8211; 2x + 4<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35337\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-7.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 7\" width=\"333\" height=\"268\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-7.png 333w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-7-300x241.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<p><strong>In Exercises 41\u201346, determine whether the quadratic function has a maximum or minimum value. Then find the value.<\/strong><br \/>\nQuestion 41.<br \/>\ny = x<sup>2<\/sup> &#8211; 4x &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-41.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 41\" width=\"565\" height=\"361\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-41.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-41-300x192.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 42.<br \/>\ny = x<sup>2<\/sup> + 6x + 10<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\ny = -x<sup>2<\/sup> &#8211; 10x &#8211; 30<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42083\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-43.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 43\" width=\"586\" height=\"400\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-43.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-43-300x205.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 44.<br \/>\ny = -x<sup>2<\/sup> + 14x &#8211; 34<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\nf(x) = -3x<sup>2<\/sup> &#8211; 6x &#8211; 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-45.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 45\" width=\"594\" height=\"397\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-45.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-45-300x201.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 46.<br \/>\nf(x) = 4x<sup>2<\/sup> &#8211; 28x + 32<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 47\u201350, determine whether the graph could represent the function. Explain.<\/strong><br \/>\nQuestion 47.<br \/>\ny = -(x + 8)(x + 3)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35338\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-8.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 8\" width=\"137\" height=\"135\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-47.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 47\" width=\"574\" height=\"137\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-47.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-47-300x72.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 48.<br \/>\ny = (x &#8211; 5)<sup>2<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35339\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-9.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 9\" width=\"130\" height=\"134\" \/><br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\ny = \\(\\frac{1}{4}\\)(x + 2)<sup>2<\/sup> &#8211; 4<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35340\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-10.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 10\" width=\"134\" height=\"129\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-49.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 49\" width=\"573\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-49.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-49-300x74.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 50.<br \/>\ny = -2(x &#8211; 1)(x + 2)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35341\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-11.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 11\" width=\"155\" height=\"128\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 51 and 52, determine which of the functions could be represented by the graph. Explain.<\/strong><br \/>\nQuestion 51.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35342\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-12.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 12\" width=\"330\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-12.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-12-300x156.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 51.1\" width=\"590\" height=\"592\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.1.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.1-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.1-150x150.png 150w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 51.2\" width=\"557\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.2.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-51.2-300x109.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 52.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35343\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-13.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 13\" width=\"335\" height=\"169\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-13.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-13-300x151.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe function h = -16t<sup>2<\/sup> + 48t represents the height h (in feet) of a kickball t seconds after it is kicked from the ground.<br \/>\na. Find the maximum height of the kickball.<br \/>\nb. Find and interpret the axis of symmetry.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-53.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 53\" width=\"518\" height=\"447\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-53.png 518w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-53-300x259.png 300w\" sizes=\"(max-width: 518px) 100vw, 518px\" \/><\/p>\n<p>Question 54.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou throw a stone from a height of 16 feet with an initial vertical velocity of 32 feet per second. The function h = -16t<sup>2<\/sup> + 32t + 16 represents the height h (in feet) of the stone after t seconds.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35344\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-14.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 14\" width=\"128\" height=\"213\" \/><br \/>\na. Find the maximum height of the stone.<br \/>\nb. Find and interpret the axis of symmetry.<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are building a rectangular brick patio surrounded by a crushed stone border with a uniform width, as shown. You purchase patio bricks to cover 140 square feet. Find the width of the border.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35345\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-15.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 15\" width=\"274\" height=\"210\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42090\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-55.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 55.1\" width=\"556\" height=\"622\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-55.1.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-55.1-268x300.png 268w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42091\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-55.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 55.2\" width=\"550\" height=\"211\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-55.2.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-55.2-300x115.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou are making a poster that will have a uniform border, as shown. The total area of the poster is 722 square inches. Find the width of the border to the nearest inch.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35346\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-16.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 16\" width=\"174\" height=\"170\" \/><br \/>\nAnswer:<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong> In Exercises 57 and 58, find the value of x. Round your answer to the nearest hundredth, if necessary.<br \/>\nQuestion 57.<br \/>\nA = 108 m<sup>2<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35347\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-17.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 17\" width=\"138\" height=\"108\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42092\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-57.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 57\" width=\"596\" height=\"608\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-57.png 596w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-57-294x300.png 294w\" sizes=\"(max-width: 596px) 100vw, 596px\" \/><\/p>\n<p>Question 58.<br \/>\nA = 288 in.<sup>2<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35349\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-18.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 18\" width=\"171\" height=\"116\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 59\u201362, solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.<\/strong><br \/>\nQuestion 59.<br \/>\n0.5x<sup>2<\/sup> + x &#8211; 2 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42093\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-59.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 59\" width=\"409\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-59.png 409w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-59-247x300.png 247w\" sizes=\"(max-width: 409px) 100vw, 409px\" \/><\/p>\n<p>Question 60.<br \/>\n0.75x<sup>2<\/sup> + 1.5x = 4<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n\\(\\frac{8}{3}\\) x &#8211; \\(\\frac{2}{3}\\)x<sup>2<\/sup> = &#8211;\\(\\frac{5}{6}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42094\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-61.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 61\" width=\"394\" height=\"699\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-61.png 394w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-61-169x300.png 169w\" sizes=\"(max-width: 394px) 100vw, 394px\" \/><\/p>\n<p>Question 62.<br \/>\n\\(\\frac{1}{4}\\)x<sup>2<\/sup> + \\(\\frac{1}{2}\\)x &#8211; \\(\\frac{5}{4}\\) = 0<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe distance d (in feet) that it takes a car to come to a complete stop can be modeled by d = 0.05s<sup>2<\/sup> + 2.2s, where s is the speed of the car (in miles per hour). A car has 168 feet to come to a complete stop. Find the maximum speed at which the car can travel.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42095\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-63.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 63\" width=\"574\" height=\"544\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-63.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-63-300x284.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 64.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nDuring a \u201cbig air\u201d competition, snowboarders launch themselves from a half-pipe, perform tricks in the air, and land back in the half-pipe. The height h (in feet) of a snowboarder above the bottom of the half-pipe can be modeled by h = -16t<sup>2<\/sup> + 24t + 16.4, where t is the time (in seconds) after the snowboarder launches into the air. The snowboarder lands 3.2 feet lower than the height of the launch. How long is the snowboarder in the air? Round your answer to the nearest tenth of a second.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35350\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-19.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 19\" width=\"266\" height=\"181\" \/><br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou have 80 feet of fencing to make a rectangular horse pasture that covers 750 square feet. A barn will be used as one side of the pasture, as shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35351\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-20.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 20\" width=\"197\" height=\"137\" \/><br \/>\na. Write equations for the amount of fencing to be used and the area enclosed by the fencing.<br \/>\nb. Use substitution to solve the system of equations from part (a). What are the possible dimensions of the pasture?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42096\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-65.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 65.1\" width=\"643\" height=\"406\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-65.1.png 643w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-65.1-300x189.png 300w\" sizes=\"(max-width: 643px) 100vw, 643px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42097\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-65.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 65.2\" width=\"686\" height=\"619\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-65.2.png 686w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-65.2-300x271.png 300w\" sizes=\"(max-width: 686px) 100vw, 686px\" \/><\/p>\n<p>Question 66.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph represents the quadratic function y = x<sup>2<\/sup> &#8211; 4x + 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35352\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-21.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 21\" width=\"160\" height=\"159\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-21.png 160w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-21-150x150.png 150w\" sizes=\"(max-width: 160px) 100vw, 160px\" \/><br \/>\na. Use the graph to estimate the x-values for which y = 3.<br \/>\nb. Explain how you can use the method of completing the square to check your estimates in part (a).<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nConsider the quadratic equation x<sup>2<\/sup> + 12x + 2 = 12.<br \/>\na. Solve the equation by graphing.<br \/>\nb. Solve the equation by completing the square.<br \/>\nc. Compare the two methods. Which do you prefer? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42098\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-67.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 67.1\" width=\"548\" height=\"573\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-67.1.png 548w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-67.1-287x300.png 287w\" sizes=\"(max-width: 548px) 100vw, 548px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42099\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-67.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 67.2\" width=\"560\" height=\"321\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-67.2.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-67.2-300x172.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 68.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nSketch the graph of the equation x<sup>2<\/sup> &#8211; 2xy + y<sup>2<\/sup> &#8211; x &#8211; y = 0. Identify the graph.<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe product of two consecutive even integers that are positive is 48. Write and solve an equation to find the integers.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42100\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-69.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 69\" width=\"567\" height=\"491\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-69.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-69-300x260.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 70.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe product of two consecutive odd integers that are negative is 195. Write and solve an equation to find the integers.<br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYou purchase stock for $16 per share. You sell the stock 30 days later for $23.50 per share. The price y (in dollars) of a share during the 30-day period can be modeled by y = -0.025x<sup>2<\/sup> + x + 16, where x is the number of days after the stock is purchased. Your friend says you could have sold the stock earlier for $23.50 per share. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35353\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-22.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 22\" width=\"270\" height=\"135\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42101\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-71.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 71\" width=\"590\" height=\"627\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-71.png 590w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-71-282x300.png 282w\" sizes=\"(max-width: 590px) 100vw, 590px\" \/><\/p>\n<p>Question 72.<br \/>\n<strong>REASONING<\/strong><br \/>\nYou are solving the equation x<sup>2<\/sup> + 9x =\ue004 18. What are the advantages of solving the equation by completing the square instead of using other methods you have learned?<br \/>\nAnswer:<\/p>\n<p>Question 73.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nYou are knitting a rectangular scarf. The pattern results in a scarf that is 60 inches long and 4 inches wide. However, you have enough yarn to knit 396 square inches. You decide to increase the dimensions of the scarf so that you will use all your yarn. The increase in the length is three times the increase in the width. What are the dimensions of your scarf?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35354\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-23.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 23\" width=\"298\" height=\"184\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42102\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 73.1\" width=\"552\" height=\"551\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.1.png 552w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.1-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.1-150x150.png 150w\" sizes=\"(max-width: 552px) 100vw, 552px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42103\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 73.2\" width=\"579\" height=\"315\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.2.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-73.2-300x163.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 74.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow many solutions does x<sup>2<\/sup> + bx = c have when c &lt; -(\\(\\frac{b}{2}\\))<sup>2<\/sup> ? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Write a recursive rule for the sequence.<\/strong><br \/>\nQuestion 75.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35355\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-24.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 24\" width=\"121\" height=\"151\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42104\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-75.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 75\" width=\"650\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-75.png 650w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-75-300x53.png 300w\" sizes=\"(max-width: 650px) 100vw, 650px\" \/><\/p>\n<p>Question 76.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35356\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-25.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 25\" width=\"133\" height=\"148\" \/><br \/>\nAnswer:<\/p>\n<p>Question 77.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35357\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-26.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 26\" width=\"129\" height=\"147\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42105\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-77.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 77\" width=\"563\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-77.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-77-300x46.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Simplify the expression \\(\\sqrt{b^{2}-4 a c}\\) for the given values.<br \/>\nQuestion 78.<br \/>\na = 3, b = -6, c = 2<br \/>\nAnswer:<\/p>\n<p>Question 79.<br \/>\na = -2, b = 4, c = 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42106\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.4-a-79.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 9 Solving Quadratic Equations 9.4 a 79\" width=\"293\" height=\"206\" \/><\/p>\n<p>Question 80.<br \/>\na = 1, b = 6, c = 4<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_9.5_Solving_Quadratic_Equations_Using_the_Quadratic_Formula\"><\/a>Lesson 9.5 Solving Quadratic Equations Using the Quadratic Formula<\/h3>\n<p><strong>Essential Question<\/strong> How can you derive a formula that can be used to write the solutions of any quadratic equation in standard form?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Deriving the Quadratic Formula<br \/>\nWork with a partner. The following steps show a method of solving ax<sup>2<\/sup> + bx + c = 0. Explain what was done in each step.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35358\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 1\" width=\"465\" height=\"386\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-1.png 465w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-1-300x249.png 300w\" sizes=\"(max-width: 465px) 100vw, 465px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Deriving the Quadratic Formula by Completing the Square<br \/>\nWork with a partner.<br \/>\na. Solve ax<sup>2<\/sup> + bx + c = 0 by completing the square. (Hint: Subtract c from each side, divide each side by a, and then proceed by completing the square.)<br \/>\nb. Compare this method with the method in Exploration 1. Explain why you think 4a and b<sup>2<\/sup> were chosen in Steps 2 and 3 of Exploration 1.<\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you derive a formula that can be used to write the solutions of any quadratic equation in standard form?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nUse the Quadratic Formula to solve each quadratic equation.<br \/>\na. x<sup>2<\/sup> + 2x &#8211; 3 = 0<br \/>\nb. x<sup>2<\/sup> &#8211; 4x + 4 = 0<br \/>\nc. x<sup>2<\/sup> + 4x + 5 = 0<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nUse the Internet to research imaginary numbers. How are they related to quadratic equations?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35359\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 2\" width=\"224\" height=\"155\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the equation using the Quadratic Formula. Round your solutions to the nearest tenth, if necessary.<\/strong><br \/>\nQuestion 1.<br \/>\nx<sup>2<\/sup> &#8211; 6x + 5 = 0<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\\(\\frac{1}{2}\\)x<sup>2<\/sup> + x &#8211; 10 = 0<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n-3x<sup>2<\/sup> + 2x + 7 = 0<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n4x<sup>2<\/sup> &#8211; 4x = -1<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nWhen were there about 60 wolf breeding pairs?<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nThe number y of bald eagle nesting pairs in a state x years since 2000 can be modeled by the function y = 0.34x<sup>2<\/sup> + 13.1x + 51.<br \/>\na. When were there about 160 bald eagle nesting pairs?<br \/>\nb. How many bald eagle nesting pairs were there in 2000?<br \/>\nAnswer:<\/p>\n<p><strong>Determine the number of real solutions of the equation.<\/strong><br \/>\nQuestion 7.<br \/>\n-x<sup>2<\/sup> + 4x &#8211; 4 = 0<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n6x<sup>2<\/sup> + 2x = -1<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n\\(\\frac{1}{2}\\)x<sup>2<\/sup> = 7x &#8211; 1<br \/>\nAnswer:<\/p>\n<p><strong>Find the number of x-intercepts of the graph of the function.<\/strong><br \/>\nQuestion 10.<br \/>\ny = -x<sup>2<\/sup> + x &#8211; 6<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ny = x<sup>2<\/sup> &#8211; x<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nf(x) = x<sup>2<\/sup> + 12x + 36<br \/>\nAnswer:<\/p>\n<p><strong>Solve the equation using any method. Explain your choice of method.<\/strong><br \/>\nQuestion 13.<br \/>\nx<sup>2<\/sup> + 11x &#8211; 12 = 0<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n9x<sup>2<\/sup> &#8211; 5 = 4<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n5x<sup>2<\/sup> &#8211; x &#8211; 1 = 0<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nx<sup>2<\/sup> = 2x &#8211; 5<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Using_the_Quadratic_Formula_9.5_Exercises\"><\/a>Solving Quadratic Equations Using the Quadratic Formula 9.5 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat formula can you use to solve any quadratic equation? Write the formula.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42107\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 1\" width=\"550\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-1.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-1-300x50.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nIn the Quadratic Formula, what is the discriminant? What does the value of the discriminant determine?<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p>In Exercises 3\u20138, write the equation in standard form. Then identify the values of a, b, and c that you would use to solve the equation using the Quadratic Formula.<br \/>\nQuestion 3.<br \/>\nx<sup>2<\/sup> = 7x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42108\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-3.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 3\" width=\"531\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-3.png 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-3-300x92.png 300w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 4.<br \/>\nx<sup>2<\/sup> &#8211; 4x = -12<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n-2x<sup>2<\/sup> + 1 = 5x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42109\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-5.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 5\" width=\"382\" height=\"308\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-5.png 382w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-5-300x242.png 300w\" sizes=\"(max-width: 382px) 100vw, 382px\" \/><\/p>\n<p>Question 6.<br \/>\n3x + 2 = 4x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n4 &#8211; 3x = -x<sup>2<\/sup> + 3x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42110\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-7.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 7\" width=\"388\" height=\"308\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-7.png 388w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-7-300x238.png 300w\" sizes=\"(max-width: 388px) 100vw, 388px\" \/><\/p>\n<p>Question 8.<br \/>\n-8x &#8211; 1 = 3x<sup>2<\/sup> + 2<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 9\u201322, solve the equation using the Quadratic Formula. Round your solutions to the nearest tenth, if necessary.<\/strong><br \/>\nQuestion 9.<br \/>\nx<sup>2<\/sup> &#8211; 12x + 36 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42111\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-9.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 9\" width=\"466\" height=\"400\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-9.png 466w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-9-300x258.png 300w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p>Question 10.<br \/>\nx<sup>2<\/sup> + 7x + 16 = 0<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nx<sup>2<\/sup> &#8211; 10x &#8211; 11 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42112\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-11.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 11\" width=\"481\" height=\"480\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-11.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-11-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-11-150x150.png 150w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><\/p>\n<p>Question 12.<br \/>\n2x<sup>2<\/sup> &#8211; x &#8211; 1 = 0<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n2x<sup>2<\/sup> &#8211; 6x + 5 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42113\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-13.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 13\" width=\"560\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-13.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-13-300x182.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 14.<br \/>\n9x<sup>2<\/sup> &#8211; 6x + 1 = 0<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n6x<sup>2<\/sup> &#8211; 13x = -6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42114\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-15.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 15\" width=\"467\" height=\"528\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-15.png 467w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-15-265x300.png 265w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/p>\n<p>Question 16.<br \/>\n-3x<sup>2<\/sup> + 6x = 4<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n1 &#8211; 8x = -16x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42115\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-17.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 17\" width=\"443\" height=\"513\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-17.png 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-17-259x300.png 259w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p>Question 18.<br \/>\nx<sup>2<\/sup> &#8211; 5x + 3 = 0<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nx<sup>2<\/sup> + 2x = 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42116\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-19.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 19\" width=\"401\" height=\"467\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-19.png 401w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-19-258x300.png 258w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><\/p>\n<p>Question 20.<br \/>\n5x<sup>2<\/sup> &#8211; 2 = 4x<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\n2x<sup>2<\/sup> + 9x + 7 = 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42117\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-21.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 21\" width=\"443\" height=\"534\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-21.png 443w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-21-249x300.png 249w\" sizes=\"(max-width: 443px) 100vw, 443px\" \/><\/p>\n<p>Question 22.<br \/>\n8x<sup>2<\/sup> + 8 = 6 &#8211; 9x<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA dolphin jumps out of the water, as shown in the diagram. The function h = -16t<sup>2<\/sup> + 26t models the height h (in feet) of the dolphin after t seconds. After how many seconds is the dolphin at a height of 5 feet?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35360\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-3.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 3\" width=\"262\" height=\"172\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42118\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-23.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 23\" width=\"565\" height=\"530\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-23.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-23-300x281.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe amount of trout y (in tons) caught in a lake from 1995 to 2014 can be modeled by the equation y = -0.08x<sup>2<\/sup> + 1.6x + 10, where x is the number of years since 1995.<br \/>\na. When were about 15 tons of trout caught in the lake?<br \/>\nb. Do you think this model can be used to determine the amounts of trout caught in future years? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 25\u201330, determine the number of real solutions of the equation.<\/strong><br \/>\nQuestion 25.<br \/>\nx<sup>2<\/sup> &#8211; 6x + 10 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42119\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-25.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 25\" width=\"550\" height=\"196\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-25.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-25-300x107.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 26.<br \/>\nx<sup>2<\/sup> &#8211; 5x &#8211; 3 = 0<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n2x<sup>2<\/sup> &#8211; 12x = -18<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42120\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-27.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 27\" width=\"556\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-27.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-27-300x131.png 300w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><\/p>\n<p>Question 28.<br \/>\n4x<sup>2<\/sup> = 4x &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n&#8211;\\(\\frac{1}{4}\\)x<sup>2<\/sup> + 4x = -2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42121\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-29.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 29\" width=\"567\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-29.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-29-300x146.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 30.<br \/>\n-5x<sup>2<\/sup> + 8x = 9<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 31\u201336, find the number of x-intercepts of the graph of the function.<\/strong><br \/>\nQuestion 31.<br \/>\ny = x<sup>2<\/sup> + 5x &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42122\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-31.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 31\" width=\"522\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-31.png 522w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-31-300x128.png 300w\" sizes=\"(max-width: 522px) 100vw, 522px\" \/><\/p>\n<p>Question 32.<br \/>\ny = 4x<sup>2<\/sup> + 4x + 1<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\ny = -6x<sup>2<\/sup> + 3x &#8211; 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42123\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-33.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 33\" width=\"550\" height=\"223\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-33.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-33-300x122.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 34.<br \/>\ny = -x<sup>2<\/sup> + 5x + 13<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nf(x) = 4x<sup>2<\/sup> + 3x &#8211; 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42124\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-35.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 35\" width=\"541\" height=\"225\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-35.png 541w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-35-300x125.png 300w\" sizes=\"(max-width: 541px) 100vw, 541px\" \/><\/p>\n<p>Question 36.<br \/>\nf(x) = 2x<sup>2<\/sup> + 8x + 8<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 37\u201344, solve the equation using any method. Explain your choice of method.<\/strong><br \/>\nQuestion 37.<br \/>\n-10x<sup>2<\/sup> + 13x = 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42125\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-37.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 37\" width=\"532\" height=\"670\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-37.png 532w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-37-238x300.png 238w\" sizes=\"(max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>Question 38.<br \/>\nx<sup>2<\/sup> &#8211; 3x &#8211; 40 = 0<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\nx<sup>2<\/sup> + 6x = 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42126\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-39.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 39\" width=\"571\" height=\"401\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-39.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-39-300x211.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 40.<br \/>\n-5x<sup>2<\/sup> = -25<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\nx<sup>2<\/sup> + x &#8211; 12 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42127\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-41.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 41\" width=\"580\" height=\"266\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-41.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-41-300x138.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 42.<br \/>\nx<sup>2<\/sup> &#8211; 4x + 1 = 0<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n4x<sup>2<\/sup> &#8211; x = 17<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42128\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-43.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 43\" width=\"562\" height=\"523\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-43.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-43-300x279.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 44.<br \/>\nx<sup>2<\/sup> + 6x + 9 = 16<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving the equation 3x<sup>2<\/sup> &#8211; 7x &#8211; 6 = 0 using the Quadratic Formul<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35361\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-4.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 4\" width=\"311\" height=\"147\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-4.png 311w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-4-300x142.png 300w\" sizes=\"(max-width: 311px) 100vw, 311px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42129\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-45.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 45\" width=\"576\" height=\"411\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-45.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-45-300x214.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving the equation -2x<sup>2<\/sup> + 9x = 4 using the Quadratic Formula.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35362\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-5.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 5\" width=\"328\" height=\"132\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-5.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-5-300x121.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA fountain shoots a water arc that can be modeled by the graph of the equation y = -0.006x<sup>2<\/sup> + 1.2x + 10, where x is the horizontal distance (in feet) from the river\u2019s north shore and y is the height (in feet) above the river. Does the water arc reach a height of 50 feet? If so, about how far from the north shore is the water arc 50 feet above the water?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35363\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-6.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 6\" width=\"265\" height=\"141\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42130\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-47.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 47\" width=\"568\" height=\"560\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-47.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-47-300x296.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nBetween the months of April and September, the number y of hours of daylight per day in Seattle, Washington, can be modeled by y = -0.00046x<sup>2<\/sup> + 0.076x + 13, where x is the number of days since April 1.<br \/>\na. Do any of the days between April and September in Seattle have 17 hours of daylight? If so, how many?<br \/>\nb. Do any of the days between April and September in Seattle have 14 hours of daylight? If so, how many?<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend uses the discriminant of the equation 2x<sup>2<\/sup> &#8211; 5x &#8211; 2 = -11 and determines that the equation has two real solutions. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42131\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-49.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 49\" width=\"553\" height=\"318\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-49.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-49-300x173.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe frame of the tent shown is defined by a rectangular base and two parabolic arches that connect the opposite corners of the base. The graph of y = -0.18x<sup>2<\/sup> + 1.6x models the height y (in feet) of one of the arches x feet along the diagonal of the base. Can a child who is 4 feet tall walk under one of the arches without having to bend over? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35364\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-7.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 7\" width=\"207\" height=\"98\" \/><br \/>\nAnswer:<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong> In Exercises 51 and 52, use the given area A of the rectangle to find the value of x. Then give the dimensions of the rectangle.<br \/>\nQuestion 51.<br \/>\nA = 91 m<sup>2<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35365\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-8.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 8\" width=\"219\" height=\"108\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42132\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-51.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 51.1\" width=\"389\" height=\"596\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-51.1.png 389w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-51.1-196x300.png 196w\" sizes=\"(max-width: 389px) 100vw, 389px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42133\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-51.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 51.2\" width=\"578\" height=\"249\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-51.2.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-51.2-300x129.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 52.<br \/>\nA = 209 ft<sup>2<\/sup><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35366\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-9.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 9\" width=\"227\" height=\"116\" \/><br \/>\nAnswer:<\/p>\n<p><strong>COMPARING METHODS<\/strong> In Exercises 53 and 54, solve the equation by (a) graphing, (b) factoring, and (c) using the Quadratic Formula. Which method do you prefer? Explain your reasoning.<br \/>\nQuestion 53.<br \/>\nx<sup>2<\/sup> + 4x + 4 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42134\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-53.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 53.1\" width=\"491\" height=\"600\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-53.1.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-53.1-246x300.png 246w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42135\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-53.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 53.2\" width=\"572\" height=\"416\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-53.2.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-53.2-300x218.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 54.<br \/>\n3x<sup>2<\/sup> + 11x + 6 = 0<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>REASONING<\/strong><br \/>\nHow many solutions does the equation ax<sup>2<\/sup> + bx + c = 0 have when a and c have different signs? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42136\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-55.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 55\" width=\"597\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-55.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-55-300x55.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>REASONING<\/strong><br \/>\nWhen the discriminant is a perfect square, are the solutions of ax<sup>2<\/sup> + bx + c = 0 rational or irrational? (Assume a, b, and c are integers.) Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>REASONING<\/strong> In Exercises 57\u201359, give a value of c for which the equation has (a) two solutions, (b) one solution, and (c) no solutions.<br \/>\nQuestion 57.<br \/>\nx<sup>2<\/sup> &#8211; 2x + c = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42137\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-57.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 57.1\" width=\"546\" height=\"615\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-57.1.png 546w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-57.1-266x300.png 266w\" sizes=\"(max-width: 546px) 100vw, 546px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42138\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-57.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 57.2\" width=\"573\" height=\"436\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-57.2.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-57.2-300x228.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 58.<br \/>\nx<sup>2<\/sup> &#8211; 8x + c = 0<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n4x<sup>2<\/sup> + 12x + c = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42139\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-59.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 59.1\" width=\"556\" height=\"618\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-59.1.png 556w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-59.1-270x300.png 270w\" sizes=\"(max-width: 556px) 100vw, 556px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42140\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-59.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 59.2\" width=\"572\" height=\"461\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-59.2.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-59.2-300x242.png 300w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>REPEATED REASONING<\/strong><br \/>\nYou use the Quadratic Formula to solve an equation.<br \/>\na. You obtain solutions that are integers. Could you have used factoring to solve the equation? Explain your reasoning.<br \/>\nb. You obtain solutions that are fractions. Could you have used factoring to solve the equation? Explain your reasoning.<br \/>\nc. Make a generalization about quadratic equations with rational solutions.<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe fuel economy y(in miles per gallon) of a car can be modeled by the equation y = -0.013x<sup>2<\/sup> + 1.25x + 5.6, where 5 \u2264 x \u2264 75 and x is the speed (in miles per hour) of the car. Find the speed(s) at which you can travel and have a fuel economy of 32 miles per gallon.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42141\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-61.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 61\" width=\"584\" height=\"588\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-61.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-61-298x300.png 298w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-61-150x150.png 150w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe depth d (in feet) of a river can be modeled by the equation d = -0.25t<sup>2<\/sup> + 1.7t + 3.5, where 0 \u2264 t \u2264 7 and t is the time (in hours) after a heavy rain begins. When is the river 6 feet deep?<br \/>\nAnswer:<\/p>\n<p><strong>ANALYZING EQUATIONS<\/strong> In Exercises 63\u201368, tell whether the vertex of the graph of the function lies above, below, or on the x-axis. Explain your reasoning without using a graph.<br \/>\nQuestion 63.<br \/>\ny = x<sup>2<\/sup> &#8211; 3x + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42142\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-63.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 63\" width=\"565\" height=\"249\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-63.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-63-300x132.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 64.<br \/>\ny = 3x<sup>2<\/sup> &#8211; 6x + 3<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\ny = 6x<sup>2<\/sup> &#8211; 2x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42143\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-65.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 65\" width=\"566\" height=\"251\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-65.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-65-300x133.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 66.<br \/>\ny = -15x<sup>2<\/sup> + 10x &#8211; 25<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\nf(x) = -3x<sup>2<\/sup> &#8211; 4x + 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42144\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-67.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 67\" width=\"562\" height=\"249\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-67.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-67-300x133.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 68.<br \/>\nf(x) = 9x<sup>2<\/sup> &#8211; 24x + 16<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\n<strong>REASONING<\/strong><br \/>\nNASA creates a weightless environment by flying a plane in a series of parabolic paths. The height h (in feet) of a plane after t seconds in a parabolic flight path can be modeled by h = -11t<sup>2<\/sup> + 700t + 21,000. The passengers experience a weightless environment when the height of the plane is greater than or equal to 30,800 feet. For approximately how many seconds do passengers experience weightlessness on such a flight? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35367\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-10.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 10\" width=\"254\" height=\"173\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42145\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-69.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 69\" width=\"553\" height=\"611\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-69.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-69-272x300.png 272w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 70.<br \/>\n<strong>WRITING EQUATIONS<\/strong><br \/>\nUse the numbers to create a quadratic equation with the solutions x = -1 and x = &#8211;\\(\\frac{1}{4}\\)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35368\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-11.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 11\" width=\"297\" height=\"121\" \/><br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA rancher constructs two rectangular horse pastures that share a side, as shown. The pastures are enclosed by 1050 feet of fencing. Each pasture has an area of 15,000 square feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35369\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-12.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 12\" width=\"318\" height=\"147\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-12.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-12-300x139.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\na. Show that y = 350 &#8211; \\(\\frac{4}{3}\\)x.<br \/>\nb. Find the possible lengths and widths of each pasture.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42146\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-71.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 71.1\" width=\"499\" height=\"619\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-71.1.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-71.1-242x300.png 242w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42147\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-71.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 71.2\" width=\"531\" height=\"612\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-71.2.png 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-71.2-260x300.png 260w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 72.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nA kicker punts a football from a height of 2.5 feet above the ground with an initial vertical velocity of 45 feet per second.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35370\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-13.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 13\" width=\"296\" height=\"108\" \/><br \/>\na. Write an equation that models this situation using the function h = -16t<sup>2<\/sup> + v<sup>0<\/sup>t + s<sup>0<\/sup>, where h is the height (in feet) of the football, t is the time (in seconds) after the football is punted, v0 is the initial vertical velocity (in feet per second), and s0 is the initial height (in feet).<br \/>\nb. The football is caught 5.5 feet above the ground, as shown in the diagram. Find the amount of time that the football is in the air.<br \/>\nAnswer:<\/p>\n<p>Question 73.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nThe solutions of the quadratic equation ax<sup>2<\/sup> + bx + c = 0 are x = \\(\\frac{-b+\\sqrt{b^{2}-4 a c}}{2 a}\\) and x = \\(\\frac{-b-\\sqrt{b^{2}-4 a c}}{2 a}\\). Find the mean of the solutions. How is the mean of the solutions related to the graph of y = ax<sup>2<\/sup> + bx + c? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42148\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-73.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 73\" width=\"579\" height=\"447\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-73.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-73-300x232.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 74.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nMatch each graph with its discriminant. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35371\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-14.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 14\" width=\"202\" height=\"464\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-14.png 202w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-14-131x300.png 131w\" sizes=\"(max-width: 202px) 100vw, 202px\" \/><br \/>\na. b<sup>2<\/sup> &#8211; 4ac &gt; 0<br \/>\nb. b<sup>2<\/sup> &#8211; 4ac = 0<br \/>\nc. b<sup>2<\/sup> &#8211; 4ac &lt; 0<br \/>\nAnswer:<\/p>\n<p>Question 75.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nYou are trying to hang a tire swing. To get the rope over a tree branch that is 15 feet high, you tie the rope to a weight and throw it over the branch. You release the weight at a height s<sub>0<\/sub> of 5.5 feet. What is the minimum initial vertical velocity v<sub>0<\/sub> needed to reach the branch? (Hint: Use the equation h = -16t<sup>2<\/sup> + v<sub>0<\/sub> t + s<sub>0<\/sub>)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42149\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-75.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 75\" width=\"575\" height=\"540\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-75.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-75-300x282.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 76.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nConsider the graph of the standard form of a quadratic function y = ax<sup>2<\/sup> + bx + c. Then consider the Quadratic Formula as given by<br \/>\nx = \\(-\\frac{b}{2 a} \\pm \\frac{\\sqrt{b^{2}-4 a c}}{2 a}\\)<br \/>\nWrite a graphical interpretation of the two parts of this formula.<br \/>\nAnswer:<\/p>\n<p>Question 77.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nFind the sum and product of \\(\\frac{-b+\\sqrt{b^{2}-4 a c}}{2 a}\\) and \\(\\frac{-b-\\sqrt{b^{2}-4 a c}}{2 a}\\). Then write a quadratic equation whose solutions have a sum of 2 and a product of \\(\\frac{1}{2}\\).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42150\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-77.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 77.1\" width=\"415\" height=\"592\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-77.1.png 415w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-77.1-210x300.png 210w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42151\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-77.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 77.2\" width=\"536\" height=\"258\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-77.2.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-77.2-300x144.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 78.<br \/>\n<strong>WRITING A FORMULA<\/strong><br \/>\nDerive a formula that can be used to find solutions of equations that have the form ax<sup>2<\/sup> + x + c = 0. Use your formula to solve -2x<sup>2<\/sup> + x + 8 = 0.<br \/>\nAnswer:<\/p>\n<p>Question 79.<br \/>\n<strong>MULTIPLE REPRESENTATIONS<\/strong><br \/>\nIf p is a solution of a quadratic equation ax<sup>2<\/sup> + bx + c = 0, then (x &#8211; p) is a factor of ax2 + bx + c.<br \/>\na. Copy and complete the table for each pair of solutions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35372\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-15.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 15\" width=\"362\" height=\"145\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-15.png 362w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-15-300x120.png 300w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><br \/>\nb. Graph the related function for each equation. Identify the zeros of the function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42152\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 79.1\" width=\"473\" height=\"473\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.1.png 473w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.1-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.1-150x150.png 150w\" sizes=\"(max-width: 473px) 100vw, 473px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42153\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 79.2\" width=\"362\" height=\"510\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.2.png 362w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.2-213x300.png 213w\" sizes=\"(max-width: 362px) 100vw, 362px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42154\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.3.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 79.3\" width=\"342\" height=\"255\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.3.png 342w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-79.3-300x224.png 300w\" sizes=\"(max-width: 342px) 100vw, 342px\" \/><\/p>\n<p><strong>CRITICAL THINKING<\/strong> In Exercises 80\u201382, find all values of k for which the equation has (a) two solutions, (b) one solution, and (c) no solutions.<br \/>\nQuestion 80.<br \/>\n2x<sup>2<\/sup> + x + 3k = 0<br \/>\nAnswer:<\/p>\n<p>Question 81.<br \/>\nx<sup>2<\/sup> = 4kx + 36 = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42155\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-81.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 81.1\" width=\"553\" height=\"607\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-81.1.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-81.1-273x300.png 273w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42156\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-81.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 81.2\" width=\"558\" height=\"631\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-81.2.png 558w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-81.2-265x300.png 265w\" sizes=\"(max-width: 558px) 100vw, 558px\" \/><\/p>\n<p>Question 82.<br \/>\nkx<sup>2<\/sup> + 5x &#8211; 16 = 0<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p>Solve the system of linear equations using any method. Explain why you chose the method.<br \/>\nQuestion 83.<br \/>\ny = -x + 4<br \/>\ny = 2x &#8211; 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42157\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-83.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 83\" width=\"562\" height=\"574\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-83.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-83-294x300.png 294w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 84.<br \/>\nx = 16 &#8211; 4y<br \/>\n3x &#8211; 4y = 8<br \/>\nAnswer:<\/p>\n<p>Question 85.<br \/>\n2x &#8211; y = 7<br \/>\n2x + 7y = 31<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42158\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-85.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 9 Solving Quadratic Equations 9.5 a 85\" width=\"531\" height=\"550\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-85.png 531w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-9-Solving-Quadratic-Equations-9.5-a-85-290x300.png 290w\" sizes=\"(max-width: 531px) 100vw, 531px\" \/><\/p>\n<p>Question 86.<br \/>\n3x &#8211; 2y = -20<br \/>\nx + 1.2y = 6.4<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_9.6_Solving_Nonlinear_Systems_of_Equations\"><\/a>Lesson 9.6 Solving Nonlinear Systems of Equations<\/h3>\n<p><strong>Essential Question <\/strong>How can you solve a system of two equations when one is linear and the other is quadratic?<\/p>\n<p><strong>EXPLORATION 1<\/strong><br \/>\nSolving a System of Equations<br \/>\nWork with a partner. Solve the system of equations by graphing each equation and finding the points of intersection.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35374\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 1\" width=\"222\" height=\"191\" \/><br \/>\nSystem of Equations<br \/>\ny = x + 2 Linear<br \/>\ny = x<sup>2<\/sup> + 2x<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Analyzing Systems of Equations<br \/>\nWork with a partner. Match each system of equations with its graph. Then solve the system of equations.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35375\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 2\" width=\"486\" height=\"369\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-2.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-2-300x228.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you solve a system of two equations when one is linear and the other is quadratic?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nWrite a system of equations (one linear and one quadratic) that has (a) no solutions, (b) one solution, and (c) two solutions. Your systems should be different from those in Explorations 1 and 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35376\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 3\" width=\"222\" height=\"151\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Solve the system by graphing.<\/strong><br \/>\nQuestion 1.<br \/>\ny = x<sup>2<\/sup> + 4x &#8211; 4<br \/>\ny = 2x &#8211; 5<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ny = -x + 6<br \/>\ny = -2x<sup>2<\/sup> &#8211; x + 3<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ny = 3x &#8211; 15<br \/>\ny = \\(\\frac{1}{2}\\)x<sup>2<\/sup> &#8211; 2x &#8211; 7<br \/>\nAnswer:<\/p>\n<p><strong>Solve the system by substitution.<\/strong><br \/>\nQuestion 4.<br \/>\ny = x<sup>2<\/sup> + 9 5.<br \/>\ny = 9<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\ny = -5x<br \/>\ny = x<sup>2<\/sup> &#8211; 3x &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\ny = -3x<sup>2<\/sup> + 2x + 1<br \/>\ny = 5 &#8211; 3x<br \/>\nAnswer:<\/p>\n<p><strong>Solve the system by elimination.<\/strong><br \/>\nQuestion 7.<br \/>\ny = x<sup>2<\/sup> + x<br \/>\ny = x + 5<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\ny = 9x<sup>2<\/sup> + 8x &#8211; 6<br \/>\ny = 5x &#8211; 4<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ny = 2x + 5<br \/>\ny = -3x<sup>2<\/sup> + x &#8211; 4<br \/>\nAnswer:<\/p>\n<p><strong>Use the method in Example 4 to approximate the solution(s) of the system to the nearest thousandth.<\/strong><br \/>\nQuestion 10.<br \/>\ny = 4<sup>x<\/sup><br \/>\ny = x<sup>2<\/sup> + x + 3<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ny = 4x<sup>2<\/sup> &#8211; 1<br \/>\ny = -2(3)<sup>x<\/sup> + 4<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\ny = x<sup>2<\/sup> + 3x<br \/>\ny = -x<sup>2<\/sup> + x + 10<br \/>\nAnswer:<\/p>\n<p><strong>Solve the equation. Round your solution(s) to the nearest hundredth.<\/strong><br \/>\nQuestion 13.<br \/>\n3<sup>x<\/sup> &#8211; 1 = x<sup>2<\/sup> &#8211; 2x + 5<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\n4x<sup>2<\/sup> + x = -2 (\\(\\frac{1}{2}\\))<sup>x<\/sup> + 5<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Nonlinear_Systems_of_Equations_9.6_Exercises\"><\/a>Solving Nonlinear Systems of Equations 9.6 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nDescribe how to use substitution to solve a system of nonlinear equations.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42173\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 1\" width=\"563\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-1.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-1-300x46.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow is solving a system of nonlinear equations similar to solving a system of linear equations? How is it different?<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 3\u20136, match the system of equations with its graph. Then solve the system.<\/strong><br \/>\nQuestion 3.<br \/>\ny = x<sup>2<\/sup> &#8211; 2x + 1<br \/>\ny = x + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42174\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 3\" width=\"597\" height=\"543\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-3.png 597w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-3-300x273.png 300w\" sizes=\"(max-width: 597px) 100vw, 597px\" \/><\/p>\n<p>Question 4.<br \/>\ny = x<sup>2<\/sup> + 3x + 2<br \/>\ny = -x &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\ny = x &#8211; 1<br \/>\ny = -x<sup>2<\/sup> + x &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42175\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 5\" width=\"581\" height=\"349\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-5.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-5-300x180.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 6.<br \/>\ny = -x + 3<br \/>\ny = -x<sup>2<\/sup> &#8211; 2x + 5<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-35377\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-4.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 4\" width=\"336\" height=\"276\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-4.png 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-4-300x246.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><\/p>\n<p><strong>In Exercises 7\u201312, solve the system by graphing.<\/strong><br \/>\nQuestion 7.<br \/>\ny = 3x<sup>2<\/sup> &#8211; 2x + 1<br \/>\ny = x + 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42176\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 7\" width=\"499\" height=\"746\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-7.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-7-201x300.png 201w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p>Question 8.<br \/>\ny = x<sup>2<\/sup> + 2x + 5<br \/>\ny = -2x &#8211; 5<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ny = -2x<sup>2<\/sup> &#8211; 4x<br \/>\ny = 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42177\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 9\" width=\"497\" height=\"515\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-9.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-9-290x300.png 290w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/p>\n<p>Question 10.<br \/>\ny = \\(\\frac{1}{2}\\)x<sup>2<\/sup> &#8211; 3x + 4<br \/>\ny = x &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ny = \\(\\frac{1}{3}\\) x<sup>2<\/sup> + 2x &#8211; 3<br \/>\ny = 2x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42178\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-11.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 11.1\" width=\"499\" height=\"514\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-11.1.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-11.1-291x300.png 291w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42179\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-11.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 11.2\" width=\"452\" height=\"250\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-11.2.png 452w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-11.2-300x166.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><\/p>\n<p>Question 12.<br \/>\ny = 4x<sup>2<\/sup> + 5x &#8211; 7<br \/>\ny = -3x + 5<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 13\u201318, solve the system by substitution.<\/strong><br \/>\nQuestion 13.<br \/>\ny = x &#8211; 5<br \/>\ny = x<sup>2<\/sup> + 4x &#8211; 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42180\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 13\" width=\"457\" height=\"479\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-13.png 457w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-13-286x300.png 286w\" sizes=\"(max-width: 457px) 100vw, 457px\" \/><\/p>\n<p>Question 14.<br \/>\ny = -3x<sup>2<\/sup><br \/>\ny = 6x + 3<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ny = -x + 7<br \/>\ny = -x<sup>2<\/sup> &#8211; 2x &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42181\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 15\" width=\"587\" height=\"555\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-15.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-15-300x284.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 16.<br \/>\ny = -x<sup>2<\/sup> + 7<br \/>\ny = 2x + 4<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\ny &#8211; 5 = -x<sup>2<\/sup><br \/>\ny = 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42182\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 17\" width=\"250\" height=\"403\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-17.png 250w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-17-186x300.png 186w\" sizes=\"(max-width: 250px) 100vw, 250px\" \/><\/p>\n<p>Question 18.<br \/>\ny = 2x<sup>2<\/sup> + 3x &#8211; 4<br \/>\ny &#8211; 4x = 2<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 19\u201326, solve the system by elimination.<\/strong><br \/>\nQuestion 19.<br \/>\ny = x<sup>2<\/sup> &#8211; 5x &#8211; 7<br \/>\ny = -5x + 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42183\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 19\" width=\"442\" height=\"454\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-19.png 442w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-19-292x300.png 292w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><\/p>\n<p>Question 20.<br \/>\ny = -3x<sup>2<\/sup> + x + 2<br \/>\ny = x + 4<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\ny = -x<sup>2<\/sup> &#8211; 2x + 2<br \/>\ny = 4x + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42184\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 21\" width=\"434\" height=\"474\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-21.png 434w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-21-275x300.png 275w\" sizes=\"(max-width: 434px) 100vw, 434px\" \/><\/p>\n<p>Question 22.<br \/>\ny = -2x<sup>2<\/sup> + x &#8211; 3<br \/>\ny = 2x &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\ny = 2x &#8211; 1<br \/>\ny = x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42185\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 23\" width=\"331\" height=\"414\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-23.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-23-240x300.png 240w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><\/p>\n<p>Question 24.<br \/>\ny = x<sup>2<\/sup> + x + 1<br \/>\ny = -x &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\ny + 2x = 0<br \/>\ny = x<sup>2<\/sup> + 4x &#8211; 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42186\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-25.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 25.1\" width=\"327\" height=\"589\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-25.1.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-25.1-167x300.png 167w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42187\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-25.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 25.2\" width=\"574\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-25.2.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-25.2-300x127.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 26.<br \/>\ny = 2x &#8211; 7<br \/>\ny + 5x = x<sup>2<\/sup> &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving the system of equations by graphing.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35378\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 5\" width=\"326\" height=\"170\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-5.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-5-300x156.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42188\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 27\" width=\"395\" height=\"321\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-27.png 395w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-27-300x244.png 300w\" sizes=\"(max-width: 395px) 100vw, 395px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in solving for one of the variables in the system.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35379\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-6.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 6\" width=\"316\" height=\"136\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-6.png 316w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-6-300x129.png 300w\" sizes=\"(max-width: 316px) 100vw, 316px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 29\u201332, use the table to describe the locations of the zeros of the quadratic function f.<\/strong><br \/>\nQuestion 29.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35380\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 7\" width=\"299\" height=\"67\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42189\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 29\" width=\"563\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-29.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-29-300x87.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 30.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35381\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-8.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 8\" width=\"296\" height=\"65\" \/><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35382\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 9\" width=\"299\" height=\"70\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42190\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-31.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 31\" width=\"570\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-31.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-31-300x88.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 32.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35383\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-10.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 10\" width=\"291\" height=\"68\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 33\u201338, use the method in Example 4 to approximate the solution(s) of the system to the nearest thousandth.<\/strong><br \/>\nQuestion 33.<br \/>\ny = x<sup>2<\/sup> + 2x + 3<br \/>\ny = 3<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42191\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-33.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 33.1\" width=\"446\" height=\"558\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-33.1.png 446w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-33.1-240x300.png 240w\" sizes=\"(max-width: 446px) 100vw, 446px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42192\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-33.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 33.2\" width=\"510\" height=\"245\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-33.2.png 510w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-33.2-300x144.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p>Question 34.<br \/>\ny = 2<sup>x<\/sup> + 5<br \/>\ny = x<sup>2<\/sup> &#8211; 3x + 1<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\ny = 2(4)<sup>x<\/sup> &#8211; 1<br \/>\ny = 3x<sup>2<\/sup> + 8x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42193\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-35.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 35.1\" width=\"609\" height=\"555\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-35.1.png 609w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-35.1-300x273.png 300w\" sizes=\"(max-width: 609px) 100vw, 609px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42194\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-35.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 35.2\" width=\"621\" height=\"724\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-35.2.png 621w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-35.2-257x300.png 257w\" sizes=\"(max-width: 621px) 100vw, 621px\" \/><\/p>\n<p>Question 36.<br \/>\ny = -x<sup>2<\/sup> &#8211; 4x &#8211; 4<br \/>\ny = -5<sup>x<\/sup> &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\ny = -x<sup>2<\/sup> &#8211; x + 5<br \/>\ny = 2x<sup>2<\/sup> + 6x &#8211; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42195\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 37.1\" width=\"753\" height=\"606\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.1.png 753w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.1-300x241.png 300w\" sizes=\"(max-width: 753px) 100vw, 753px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42196\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 37.2\" width=\"788\" height=\"626\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.2.png 788w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.2-300x238.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-37.2-768x610.png 768w\" sizes=\"(max-width: 788px) 100vw, 788px\" \/><\/p>\n<p>Question 38.<br \/>\ny = 2x<sup>2<\/sup> + x &#8211; 8<br \/>\ny = x<sup>2<\/sup> &#8211; 5<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 39\u201346, solve the equation. Round your solution(s) to the nearest hundredth.<\/strong><br \/>\nQuestion 39.<br \/>\n3x + 1 = x<sup>2<\/sup> + 7x &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42197\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-39.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 39\" width=\"544\" height=\"504\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-39.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-39-300x278.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 40.<br \/>\n-x<sup>2<\/sup> + 2x = -2x + 5<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\nx<sup>2<\/sup> &#8211; 6x + 4 = -x<sup>2<\/sup> &#8211; 2x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42198\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-41.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 41\" width=\"575\" height=\"269\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-41.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-41-300x140.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 42.<br \/>\n2x<sup>2<\/sup> + 8x + 10 = -x<sup>2<\/sup> &#8211; 2x + 5<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n-4 (\\(\\frac{1}{2}\\))<sup>x<\/sup> = -x<sup>2<\/sup> &#8211; 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42199\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-43.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 43\" width=\"574\" height=\"307\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-43.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-43-300x160.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p>Question 44.<br \/>\n1.5(2)<sup>x<\/sup> &#8211; 3 = -x<sup>2<\/sup> + 4x<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n8<sup>x-2<\/sup> + 3 = 2 (\\(\\frac{3}{2}\\))<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42200\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-45.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 45\" width=\"575\" height=\"512\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-45.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-45-300x267.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 46.<br \/>\n-0.5(4)<sup>x<\/sup> = 5<sup>x<\/sup> &#8211; 6<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nSolve the system in Exercise 37 using substitution. Compare the exact solutions to the approximated solutions.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42201\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-47.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 47.1\" width=\"357\" height=\"628\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-47.1.png 357w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-47.1-171x300.png 171w\" sizes=\"(max-width: 357px) 100vw, 357px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42202\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-47.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 47.2\" width=\"528\" height=\"628\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-47.2.png 528w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-47.2-252x300.png 252w\" sizes=\"(max-width: 528px) 100vw, 528px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>COMPARING METHODS<\/strong><br \/>\nSolve the system in Exercise 38 using elimination. Compare the exact solutions to the approximated solutions.<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe attendances y for two movies can be modeled by the following equations, where x is the number of days since the movies opened.<br \/>\ny = -x<sup>2<\/sup> + 35x + 100 Movie A<br \/>\ny = -5x + 275 Movie B<br \/>\nWhen is the attendance for each movie the same?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42203\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-49.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 49\" width=\"575\" height=\"334\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-49.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-49-300x174.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 50.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nYou and a friend are driving boats on the same lake. Your path can be modeled by the equation y = -x<sup>2<\/sup> &#8211; 4x &#8211; 1, and your friend\u2019s path can be modeled by the equation y = -2x + 8. Do your paths cross each other? If so, what are the coordinates of the point(s) where the paths meet?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35384\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 11\" width=\"297\" height=\"138\" \/><br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe arch of a bridge can be modeled by y = -0.002x<sup>2<\/sup> + 1.06x, where x is the distance (in meters) from the left pylons and y is the height (in meters) of the arch above the water. The road can be modeled by the equation y = 52. To the nearest meter, how far from the left pylons are the two points where the road intersects the arch of the bridge?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35385\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-12.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 12\" width=\"331\" height=\"159\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-12.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-12-300x144.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42204\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-51.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 51\" width=\"577\" height=\"598\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-51.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-51-289x300.png 289w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 52.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says that a system of equations consisting of a linear equation and a quadratic equation can have zero, one, two, or infinitely many solutions. Is your friend correct? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>COMPARING METHODS<\/strong> In Exercises 53 and 54, solve the system of equations by (a) graphing, (b) substitution, and (c) elimination. Which method do you prefer? Explain your reasoning.<br \/>\nQuestion 53.<br \/>\ny = 4x + 3<br \/>\ny = x<sup>2<\/sup> + 4x &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42205\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-53.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 53.1\" width=\"506\" height=\"647\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-53.1.png 506w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-53.1-235x300.png 235w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42206\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-53.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 53.2\" width=\"579\" height=\"620\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-53.2.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-53.2-280x300.png 280w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 54.<br \/>\ny = x<sup>2<\/sup> &#8211; 5<br \/>\ny = -x + 7<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe function y = -x<sup>2<\/sup> + 65x + 256 models the number y of subscribers to a website, where x is the number of days since the website launched. The number of subscribers to a competitor\u2019s website can be modeled by a linear function. The websites have the same number of subscribers on Days 1 and 34.<br \/>\na. Write a linear function that models the number of subscribers to the competitor\u2019s website.<br \/>\nb. Solve the system to verify the function from part (a).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42207\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-55.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 55.1\" width=\"564\" height=\"613\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-55.1.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-55.1-276x300.png 276w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42208\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-55.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 55.2\" width=\"586\" height=\"326\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-55.2.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-55.2-300x167.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe diagram shows the graphs of two equations in a system that has one solution.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35386\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 13\" width=\"195\" height=\"186\" \/><br \/>\na. How many solutions will the system have when you change the linear equation to y = c + 2?<br \/>\nb. How many solutions will the system have when you change the linear equation to y = c &#8211; 2?<br \/>\nAnswer:<\/p>\n<p>Question 57.<br \/>\n<strong>WRITING<\/strong><br \/>\nA system of equations consists of a quadratic equation whose graph opens up and a quadratic equation whose graph opens down. Describe the possible numbers of solutions of the system. Sketch examples to justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42209\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-57.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 57\" width=\"588\" height=\"359\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-57.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-57-300x183.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 58.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe population of a country is 2 million people and increases by 3% each year. The country\u2019s food supply is sufficient to feed 3 million people and increases at a constant rate that feeds 0.25 million additional people each year.<br \/>\na. When will the country first experience a food shortage?<br \/>\nb. The country doubles the rate at which its food supply increases. Will food shortages still occur? If so, in what year?<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n<strong>ANALYZING GRAPHS<\/strong><br \/>\nUse the graphs of the linear and quadratic functions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35387\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-14.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 14\" width=\"245\" height=\"194\" \/><br \/>\na. Find the coordinates of point A.<br \/>\nb. Find the coordinates of point B.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42210\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-59.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 59.1\" width=\"450\" height=\"621\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-59.1.png 450w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-59.1-217x300.png 217w\" sizes=\"(max-width: 450px) 100vw, 450px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42211\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-59.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 59.2\" width=\"427\" height=\"276\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-59.2.png 427w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-59.2-300x194.png 300w\" sizes=\"(max-width: 427px) 100vw, 427px\" \/><\/p>\n<p>Question 60.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nIs it possible for a system of two quadratic equations to have exactly three solutions? exactly four solutions? Explain your reasoning. (Hint: Rotations of the graphs of quadratic equations still represent quadratic equations.)<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nSolve the system of three equations shown.<br \/>\ny = 2x &#8211; 8<br \/>\ny = x<sup>2<\/sup> &#8211; 4x &#8211; 3<br \/>\ny = -3(2)<sup>x<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42212\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-61.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 61\" width=\"620\" height=\"366\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-61.png 620w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-61-300x177.png 300w\" sizes=\"(max-width: 620px) 100vw, 620px\" \/><\/p>\n<p>Question 62.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nFind the point(s) of intersection, if any, of the line y = -x &#8211; 1 and the circle x<sup>2<\/sup> + y<sup>2<\/sup> = 41.<br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Graph the system of linear inequalities.<\/strong><br \/>\nQuestion 63.<br \/>\ny &gt; 2x<br \/>\ny &gt; -x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42213\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-63.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 63\" width=\"241\" height=\"235\" \/><\/p>\n<p>Question 64.<br \/>\ny \u2265 4x + 1<br \/>\ny \u2264 7<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\ny &#8211; 3 \u2264 -2x<br \/>\ny + 5 &lt; 3x Answer: Question 66. x + y &gt; -6<br \/>\n2y \u2264 3x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42214\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-65.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 65\" width=\"486\" height=\"346\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-65.png 486w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-65-300x214.png 300w\" sizes=\"(max-width: 486px) 100vw, 486px\" \/><\/p>\n<p><strong>Graph the function. Describe the domain and range.<\/strong><br \/>\nQuestion 67.<br \/>\ny = 3x<sup>2<\/sup> + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42215\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-67.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 67\" width=\"467\" height=\"428\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-67.png 467w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-67-300x275.png 300w\" sizes=\"(max-width: 467px) 100vw, 467px\" \/><\/p>\n<p>Question 68.<br \/>\ny = -x<sup>2<\/sup> &#8211; 6x<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\ny = -2x<sup>2<\/sup> + 12x &#8211; 7<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-42216\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-69.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 a 69\" width=\"491\" height=\"423\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-69.png 491w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-a-69-300x258.png 300w\" sizes=\"(max-width: 491px) 100vw, 491px\" \/><\/p>\n<p>Question 70.<br \/>\ny = 5x<sup>2<\/sup> + 10x &#8211; 3<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Performance_Task:_Form_Matters\"><\/a>Solving Quadratic Equations Performance Task: Form Matters<\/h3>\n<p><strong>9.4\u20139.6 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35388\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 15\" width=\"651\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-15.png 651w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-15-300x26.png 300w\" sizes=\"(max-width: 651px) 100vw, 651px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\nSection 9.4<br \/>\nCompleting the Square, p. 506<\/p>\n<p>Section 9.5<br \/>\nQuadratic Formula, p. 516<br \/>\nInterpreting the Discriminant, p. 518<\/p>\n<p>Section 9.6<br \/>\nSolving Systems of Nonlinear Equations, p. 526<\/p>\n<p><strong>Mathematical Practices<\/strong><br \/>\nQuestion 1.<br \/>\nHow does your answer to Exercise 74 on page 514 help create a shortcut when solving some quadratic equations by completing the square?<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nWhat logical progression led you to your answer in Exercise 55 on page 522?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nCompare the methods used to solve Exercise 53 on page 532. Discuss the similarities and differences among the methods.<br \/>\nAnswer:<\/p>\n<p><strong>Performance Task Form Matters<\/strong><\/p>\n<p>Each form of a quadratic function has its pros and cons. Using one form, you can easily find the vertex, but the zeros are more difficult to find. Using another form, you can easily find the y-intercept, but the vertex is more difficult to find. Which form would you use in different situations? How can you convert one form into another? To explore the answers to these questions and more, go to.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35389\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-16.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 9 Solving Quadratic Equations 9.6 16\" width=\"364\" height=\"279\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-16.png 364w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-9-Solving-Quadratic-Equations-9.6-16-300x230.png 300w\" sizes=\"(max-width: 364px) 100vw, 364px\" \/><\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Chapter_Review\"><\/a>Solving Quadratic Equations Chapter Review<\/h3>\n<p><strong>9.1 Properties of Radicals (pp. 479\u2013488)<\/strong><\/p>\n<p>Simplify the expression.<br \/>\nQuestion 1.<br \/>\n\\(\\sqrt{72 p^{7}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n\\(\\sqrt{\\frac{45}{7 y}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n\\(\\sqrt[3]{\\frac{125 x^{11}}{4}}\\)<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\n\\(\\frac{8}{\\sqrt{6}+2}\\)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n4\\(\\sqrt{3}\\) + 5\\(\\sqrt{12}\\)<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n15\\(\\sqrt [ 3 ]{ 2 }\\) &#8211; 2\\(\\sqrt [ 3 ]{ 54 }\\)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n(3\\(\\sqrt{7}\\) + 5)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\n\\(\\sqrt{6}\\)(\\(\\sqrt{18}\\) + \\(\\sqrt{8}\\))<br \/>\nAnswer:<\/p>\n<p><strong>9.2 Solving Quadratic Equations by Graphing (pp. 489\u2013496)<\/strong><\/p>\n<p><strong>Solve the equation by graphing<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35390\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-cr-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations cr 9\" width=\"279\" height=\"191\" \/><br \/>\nQuestion 9.<br \/>\nx<sup>2<\/sup> &#8211; 9x + 18 = 0<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nx<sup>2<\/sup> &#8211; 2x = -4<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n-8x &#8211; 16 = x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nThe graph of f(x) = (x + 1)(x<sup>2<\/sup> + 2x &#8211; 3) is shown. Find the zeros of f.<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nGraph f(x) = x<sup>2<\/sup> + 2x &#8211; 5. Approximate the zeros of f to the nearest tenth.<br \/>\nAnswer:<\/p>\n<p><strong>9.3 Solving Quadratic Equations Using Square Roots (pp. 497\u2013502)<\/strong><\/p>\n<p><strong>Solve the equation using square roots. Round your solutions to the nearest hundredth, if necessary.<\/strong><br \/>\nQuestion 14.<br \/>\nx<sup>2<\/sup> + 5 = 17<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nx<sup>2<\/sup> &#8211; 14 = -14<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\n(x + 2)<sup>2<\/sup> = 64<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n4x<sup>2<\/sup> + 25 = -75<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\n(x &#8211; 1)<sup>2<\/sup> = 0<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n19 = 30 &#8211; 5x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>9.4 Solving Quadratic Equations by Completing the Square (pp. 505\u2013514)<\/strong><\/p>\n<p><strong>Solve the equation by completing the square. Round your solutions to the nearest hundredth, if necessary.<\/strong><br \/>\nQuestion 20.<br \/>\nx<sup>2<\/sup> + 6x &#8211; 40 = 0<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nx<sup>2<\/sup> + 2x + 5 = 4<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\n2x<sup>2<\/sup> &#8211; 4x = 10<br \/>\nAnswer:<\/p>\n<p>Determine whether the quadratic function has a maximum or minimum value. Then find the value.<br \/>\nQuestion 23.<br \/>\ny = -x<sup>2<\/sup> + 6x &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\nf(x) = x<sup>2<\/sup> + 4x + 11<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\ny = 3x<sup>2<\/sup> &#8211; 24x + 15<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\nThe width w of a credit card is 3 centimeters shorter than the length \u2113. The area is 46.75 square centimeters. Find the perimeter.<br \/>\nAnswer:<\/p>\n<p><strong>9.5 Solving Quadratic Equations Using the Quadratic Formula (pp. 515\u2013524)<\/strong><\/p>\n<p><strong>Solve the equation using the Quadratic Formula. Round your solutions to the nearest tenth, if necessary.<\/strong><br \/>\nQuestion 27.<br \/>\nx<sup>2<\/sup>+ 2x &#8211; 15 = 0<br \/>\nans;<\/p>\n<p>Question 28.<br \/>\n2x<sup>2<\/sup> &#8211; x + 8 = 16<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n-5x<sup>2<\/sup> + 10x = 5<br \/>\nans;<\/p>\n<p>Find the number of x-intercepts of the graph of the function.<br \/>\nQuestion 30.<br \/>\ny = -x<sup>2<\/sup> + 6x &#8211; 9<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\ny = 2x<sup>2<\/sup> + 4x + 8<br \/>\nAnswer:<\/p>\n<p>Question 32.<br \/>\ny = &#8211; \\(\\frac{1}{2}\\)x<sup>2<\/sup> + 2x<br \/>\nAnswer:<\/p>\n<p><strong>9.6 Solving Nonlinear Systems of Equations (pp. 525\u2013532)<\/strong><\/p>\n<p><strong>Solve the system using any method.<\/strong><br \/>\nQuestion 33.<br \/>\ny = x<sup>2<\/sup> &#8211; 2x &#8211; 4<br \/>\ny = -5<br \/>\nAnswer:<\/p>\n<p>Question 34.<br \/>\ny = x<sup>2<\/sup> &#8211; 9<br \/>\ny = 2x + 5<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\ny = 2(\\(\\frac{1}{2}\\))<sup>x<\/sup> &#8211; 5<br \/>\ny = -x<sup>2<\/sup> &#8211; x + 4<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Chapter_Test\"><\/a>Solving Quadratic Equations Chapter Test<\/h3>\n<p><strong>Solve the equation using any method. Explain your choice of method.<\/strong><br \/>\nQuestion 1.<br \/>\nx<sup>2<\/sup> &#8211; 121 = 0<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nx<sup>2<\/sup> &#8211; 6x = 10<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n-2x<sup>2<\/sup> + 3x + 7 = 0<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nx<sup>2<\/sup> &#8211; 7x + 12 = 0<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n5x<sup>2<\/sup> + x &#8211; 4 = 0<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n(4x + 3)<sup>2<\/sup> = 16<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nDescribe how you can use the method of completing the square to determine whether the function f(x) = 2x<sup>2<\/sup> + 4x &#8211; 6 can be represented by the graph shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35391\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-ct-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations ct 7\" width=\"141\" height=\"145\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nWrite an expression involving radicals in which a conjugate can be used to simplify the expression.<br \/>\nAnswer:<\/p>\n<p><strong>Solve the system using any method.<\/strong><br \/>\nQuestion 9.<br \/>\ny = x<sup>2<\/sup> &#8211; 4x &#8211; 2<br \/>\ny = -4x + 2<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\ny = -5x<sup>2<\/sup> + x &#8211; 1<br \/>\ny = -7<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ny = \\(\\frac{1}{2}\\)(4)<sup>x<\/sup> + 1<br \/>\ny = x<sup>2<\/sup> &#8211; 2x + 4<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nA skier leaves an 8-foot-tall ramp with an initial vertical velocity of 28 feet per second. The function h = -16t<sup>2<\/sup> + 28t + 8 represents the height h (in feet) of the skier after t seconds. The skier has a perfect landing. How many points does the skier earn?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35392\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-ct-12.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations ct 12\" width=\"260\" height=\"120\" \/><br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nAn amusement park ride lifts seated riders 265 feet above the ground. The riders are then dropped and experience free fall until the brakes are activated 105 feet above the ground. The function h = -16t<sup>2<\/sup> + 265 represents the height h (in feet) of the riders t seconds after they are dropped. How long do the riders experience free fall? Round your solution to the nearest hundredth.<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nWrite an expression in simplest form that represents the area of the painting shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35393\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations-ct-14.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations ct 14\" width=\"265\" height=\"116\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nExplain how you can determine the number of times the graph of y = 5x<sup>2<\/sup> &#8211; 10x + 5 intersects the x-axis without graphing or solving an equation.<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nConsider the quadratic equation ax<sup>2<\/sup> + bx + c = 0 Find values of a, b, and c so that the graph of its related function has (a) two x x-intercepts, (b) one x-intercepts.and (c) no x-intercepts.<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nThe numbers y of two types of bacteria after x hours are represented by the models below.<br \/>\ny = 3x<sup>2<\/sup> + 8x + 20 Type A<br \/>\ny = 27x + 60 Type B<br \/>\na. When are there 400 Type A bacteria?<br \/>\nb. When are the number of Type A and Type B bacteria the same?<br \/>\nc. When are there more Type A bacteria than Type B? When are there more Type B bacteria than Type A? Use a graph to support your answer.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Solving_Quadratic_Equations_Cumulative_Assessment\"><\/a>Solving Quadratic Equations Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nThe graphs of four quadratic functions are shown. Determine whether the discriminants of the equations formed by setting each function equal to zero are positive, negative, or zero.f(x) = 0, g(x) = 0, h(x) = 0, and j(x) = 0<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35394\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations ca 1\" width=\"190\" height=\"190\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-1.png 190w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-1-150x150.png 150w\" sizes=\"(max-width: 190px) 100vw, 190px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nThe function f(x) = a(1.08)<sup>x<\/sup> represents the total amount of money (in dollars) in Account A after x years. The function g(x) = 600(b)<sup>x<\/sup> represents the total amount of money (in dollars) in Account B after x years. Fill in values for a and b so that each statement is true.<br \/>\na. When a = ____ and b = ____, Account B has a greater initial amount and increases at a faster rate than Account A.<br \/>\nb. When a = ____ and b = ____, Account B has a lesser initial amount than Account A but increases at a faster rate than Account A.<br \/>\nc. When a = ____ and b = ____, Account B and Account A have the same initial amount, and Account B increases at a slower rate than Account A.<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nYour friend claims to be able to find the radius r of each figure, given the surface area S. Do you support your friend\u2019s claim? Justify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35395\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations ca 3\" width=\"481\" height=\"148\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-3.png 481w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-3-300x92.png 300w\" sizes=\"(max-width: 481px) 100vw, 481px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nThe tables represent the numbers of items sold at a concession stand on days with different average temperatures. Determine whether the data represented by each table show a positive, a negative, or no correlation.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35396\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-4.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations ca 4\" width=\"524\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-4.png 524w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-4-300x90.png 300w\" sizes=\"(max-width: 524px) 100vw, 524px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nWhich graph shows exponential growth?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35397\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations ca 5\" width=\"483\" height=\"391\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-5.png 483w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-5-300x243.png 300w\" sizes=\"(max-width: 483px) 100vw, 483px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nWhich statement best describes the solution(s) of the system of equations?<br \/>\ny = x<sup>2<\/sup> + 2x &#8211; 8<br \/>\ny = 5x + 2<br \/>\nA. The graphs intersect at one point, (-2, -8). So, there is one solution.<br \/>\nB. The graphs intersect at two points, (-2, -8) and (5, 27). So, there are two solutions.<br \/>\nC. The graphs do not intersect. So, there is no solution.<br \/>\nD. The graph of y = x<sup>2<\/sup> + 2x &#8211; 8 has two x-intercepts. So, there are two solutions.<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nWhich expressions are in simplest form?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35398\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 9 Solving Quadratic Equations ca 7\" width=\"433\" height=\"127\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-7.png 433w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-9-Solving-Quadratic-Equations-ca-7-300x88.png 300w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nThe domain of the function shown is all integers in the interval -3 &lt; x \u2264 3. Find all the ordered pairs that are solutions of the equation y = f(x).<br \/>\nf(x) = 4x &#8211; 5<br \/>\nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>If you are seeking homework help to complete the chapter 9 Solving Quadratic Equations Questions then stay connected with us. Here we have shared the best solution for your concerns ie., Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations Pdf Exercise-wise. This guide will aid students in enhancing their problem-solving and subject &#8230; <a title=\"Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-9\/\" aria-label=\"More on Big Ideas Math Algebra 1 Answers Chapter 9 Solving Quadratic Equations\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":89135,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[4],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-9-Solving-Quadratic-Equations.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35266"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=35266"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35266\/revisions"}],"predecessor-version":[{"id":90380,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35266\/revisions\/90380"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89135"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=35266"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=35266"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=35266"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}