{"id":35943,"date":"2022-04-01T16:30:13","date_gmt":"2022-04-01T11:00:13","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=35943"},"modified":"2022-04-07T11:42:39","modified_gmt":"2022-04-07T06:12:39","slug":"big-ideas-math-algebra-1-answers-chapter-8","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-8\/","title":{"rendered":"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions"},"content":{"rendered":"<p><strong>Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions Pdf<\/strong> of all exercises along with extra practice sections, quizzes, chapter tests, cumulative assessment, etc. are provided here. Students who are searching for the perfect study guide to enhance their math skills can refer to this Big ideas math algebra 1 ch 8 answer key.<\/p>\n<p>Graphing quadratic functions concepts can be pretty easy by solving from the Big ideas math book answers of Algebra 1 Chapter 8 Graphing Quadratic Functions. The main aim of providing this Ch 8 Graphing Quadratic Functions <strong><a href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers\/\">Big Ideas Math Algebra 1 Answers<\/a> <\/strong>is to offer quality education to the students and support them to grow high &amp; become pro in math concepts.<\/p>\n<h2 class=\"entry-title\">Big Ideas Math Book Algebra 1 Answer Key Ch 8 Graphing Quadratic Functions<\/h2>\n<p>By using the BIM Textbook Solutions Algebra 1 Chapter 8 Graphing Quadratic Functions, you can solve all questions at the time of homework &amp; assignments. Here is the list of <strong>topic-wise Big Ideas math Algebra 1 ch 8 Graphing Quadratic Functions Answer Key<\/strong> that helps you learn and understand every single concept of algebra 1 maths.<\/p>\n<p><em>BigIdeasMath Algebra 1 Graphing Quadratic Functions Chapter 8 Exercise questions and answers<\/em> are prepared by subject experts based on the Common Core Standards. So, students can easily solve all exercise questions, Questions from Practice Test, Chapter Test, Cumulative Practice, Performance Test, etc. covered in BIM Algebra 1 Ch 8 Answer key<\/p>\n<ul>\n<li><a href=\"#Graphing_Quadratic_Functions_Maintaining_Mathematical_Proficiency\">Graphing Quadratic Functions Maintaining Mathematical Proficiency &#8211; Page 417<\/a><\/li>\n<li><a href=\"#Graphing_Quadratic_Functions_Mathematical_Practices\">Graphing Quadratic Functions Mathematical Practices &#8211; Page 418<\/a><\/li>\n<li><a href=\"#Lesson_8.1_Graphing_f(x)_=_ax2\">Lesson 8.1 Graphing f(x) = ax2 &#8211; Page (419-424)<\/a><\/li>\n<li><a href=\"#Graphing_f(x)_=_ax2_8.1_Exercises\">Graphing f(x) = ax2 8.1 Exercises &#8211; Page (423-424)<\/a><\/li>\n<li><a href=\"#Lesson_8.2_Graphing_f(x)_=_ax2_+_c\">Lesson 8.2 Graphing f(x) = ax2 + c &#8211; Page (425-430)<\/a><\/li>\n<li><a href=\"#Graphing_f(x)_=_ax2_+_c_8.2_Exercises\">Graphing f(x) = ax2 + c 8.2 Exercises &#8211; Page (429-430)<\/a><\/li>\n<li><a href=\"#Lesson_8.3_Graphing_f(x)_=_ax2_+_bx_+_c\">Lesson 8.3 Graphing f(x) = ax2 + bx + c &#8211; Page (431-438)<\/a><\/li>\n<li><a href=\"#Graphing_f(x)_=_ax2_+_bx_+_c_8.3_Exercises\">Graphing f(x) = ax2 + bx + c 8.3 Exercises &#8211; Page (436-438)<\/a><\/li>\n<li><a href=\"#Graphing_Quadratic_Functions_Study_Skills:_Learning_Visually\">Graphing Quadratic Functions Study Skills: Learning Visually &#8211; Page 439<\/a><\/li>\n<li><a href=\"#Graphing_Quadratic_Functions_8.1_-_8.3_Quiz\">Graphing Quadratic Functions 8.1 &#8211; 8.3 Quiz &#8211; Page 440<\/a><\/li>\n<li><a href=\"#Lesson_8.4_Graphing_f(x)_=_a(x_-_h)2_+_k\">Lesson 8.4 Graphing f(x) = a(x &#8211; h)2 + k &#8211; Page (441-448)<\/a><\/li>\n<li><a href=\"#Graphing_f(x)_=_a(x_-_h)2_+_k_8.4_Exercises\">Graphing f(x) = a(x &#8211; h)2 + k 8.4 Exercises &#8211; Page (446-448)<\/a><\/li>\n<li><a href=\"#Lesson_8.5_Using_Intercept_Form\">Lesson 8.5 Using Intercept Form &#8211; Page (449-458)<\/a><\/li>\n<li><a href=\"#Using_Intercept_Form_8.5_Exercises\">Using Intercept Form 8.5 Exercises &#8211; Page (455-458)<\/a><\/li>\n<li><a href=\"#Lesson_8.6_Comparing_Linear,_Exponential,_and_Quadratic_Functions\">Lesson 8.6 Comparing Linear, Exponential, and Quadratic Functions &#8211; Page (459-468)<\/a><\/li>\n<li><a href=\"#Comparing_Linear,_Exponential,_and_Quadratic_Functions_8.6_Exercises\">Comparing Linear, Exponential, and Quadratic Functions 8.6 Exercises &#8211; Page (465-468)<\/a><\/li>\n<li><a href=\"#Graphing_Quadratic_Functions_Performance_Task:_Asteroid_Aim\">Graphing Quadratic Functions Performance Task: Asteroid Aim &#8211; Page 469<\/a><\/li>\n<li><a href=\"#Graphing_Quadratic_Functions_Chapter_Review\">Graphing Quadratic Functions Chapter Review &#8211; Page (470-472)<\/a><\/li>\n<li><a href=\"#Graphing_Quadratic_Functions_Chapter_Test\">Graphing Quadratic Functions Chapter Test &#8211; Page 473\u00a0<\/a><\/li>\n<li><a href=\"#Graphing_Quadratic_Functions_Cumulative_Assessment\">Graphing Quadratic Functions Cumulative Assessment &#8211; Page (474-475)<\/a><\/li>\n<\/ul>\n<h3><a id=\"Graphing_Quadratic_Functions_Maintaining_Mathematical_Proficiency\"><\/a>Graphing Quadratic Functions Maintaining Mathematical Proficiency<\/h3>\n<p><strong>Graph the linear equation.<\/strong><\/p>\n<p>Question 1.<br \/>\ny = 2x &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ny = -3x + 4<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ny = &#8211; \\(\\frac{1}{2}\\)x &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\ny = x + 5<br \/>\nAnswer:<\/p>\n<p><strong>Evaluate the expression when x = \u22122.<\/strong><br \/>\nQuestion 5.<br \/>\n5x<sup>2<\/sup> &#8211; 9<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\n3x<sup>2<\/sup> + x &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n-x<sup>2<\/sup> + 4x + 1<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nx<sup>2<\/sup> + 8x + 5<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n-2x<sup>2<\/sup> &#8211; 4x + 3<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\n-4x<sup>2<\/sup> + 2x &#8211; 6<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n<strong>ABSTRACT REASONING<\/strong><br \/>\nComplete the table. Find a pattern in the differences of consecutive y-values. Use the pattern to write an expression for y when x = 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 1\" width=\"254\" height=\"71\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_Quadratic_Functions_Mathematical_Practices\"><\/a>Graphing Quadratic Functions Mathematical Practices<\/h3>\n<p>Mathematically proficient students try special cases of the original problem to gain insight into its solution.<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Graph the quadratic function. Then describe its graph.<\/strong><br \/>\nQuestion 1.<br \/>\ny = -x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ny = 2x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nf(x) = 2x<sup>2<\/sup> + 1<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nf(x) = 2x<sup>2<\/sup> &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nf(x) = \\(\\frac{1}{2}\\)x<sup>2<\/sup> + 4x + 3<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nf(x) = \\(\\frac{1}{2}\\) x<sup>2<\/sup> &#8211; 4x + 3<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ny = -2(x + 1)<sup>2<\/sup> + 1<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\ny = -2(x &#8211; 1)<sup>2<\/sup> + 1<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nHow are the graphs in Monitoring Progress Questions 1-8 similar? How are they different?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_8.1_Graphing_f(x)_=_ax2\"><\/a>Lesson 8.1 Graphing f(x) = ax<sup>2<\/sup><\/h3>\n<p><strong>Essential Question<\/strong> What are some of the characteristics of the graph of a quadratic function of the form f(x) = ax<sup>2<\/sup>?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Graphing Quadratic Functions<br \/>\nWork with a partner. Graph each quadratic function. Compare each graph to the graph of f(x) = x<sup>2<\/sup>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35947\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 1\" width=\"510\" height=\"502\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-1.png 510w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-1-300x295.png 300w\" sizes=\"(max-width: 510px) 100vw, 510px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 2.<br \/>\nWhat are some of the characteristics of the graph of a quadratic function of the form f(x) = ax<sup>2<\/sup>?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nHow does the value of a affect the graph of f(x) = ax<sup>2<\/sup>? Consider 0 &lt; a &lt; 1, a&gt; 1, -1 &lt; a &lt; 0, and a &lt; -1. Use a graphing calculator to verify your answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35948\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 2\" width=\"219\" height=\"175\" \/><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nThe figure shows the graph of a quadratic function of the form y = ax<sup>2<\/sup>. Which of the intervals in Question 3 describes the value of a? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 3\" width=\"189\" height=\"141\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Identify characteristics of the quadratic function and its graph.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-4.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 4\" width=\"191\" height=\"188\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35951\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 5\" width=\"187\" height=\"187\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-5.png 187w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-5-150x150.png 150w\" sizes=\"(max-width: 187px) 100vw, 187px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<br \/>\n<\/strong>Question 3.<br \/>\ng(x) = 5x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nh(x) = \\(\\frac{1}{3}\\)x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nn(x) = \\(\\frac{3}{2}\\)x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\np(x) = -3x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nq(x) = -0.1x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\ng(x) = &#8211;\\(\\frac{1}{4}\\)x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nThe cross section of a spotlight can be modeled by the graph of y = 0.5x<sup>2<\/sup>, where x and y are measured in inches and -2 \u2264 x \u2264 2. Find the width and depth of the spotlight.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_f(x)_=_ax2_8.1_Exercises\"><\/a>Graphing f(x) = ax<sup>2<\/sup> 8.1 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nWhat is the U-shaped graph of a quadratic function called?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43809\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 1\" width=\"519\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-1.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-1-300x35.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nWhen does the graph of a quadratic function open up? open down?<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3 and 4, identify characteristics of the quadratic function and its graph.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-6.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 6\" width=\"190\" height=\"194\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43810\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 3\" width=\"550\" height=\"106\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-3.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-3-300x58.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 7\" width=\"192\" height=\"190\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 5\u201312, graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 5.<br \/>\ng(x) = 6x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43811\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 5\" width=\"583\" height=\"476\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-5.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-5-300x245.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 6.<br \/>\nb(x) = 2.5x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nh(x) = \\(\\frac{1}{4}\\)x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43812\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 7\" width=\"586\" height=\"463\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-7.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-7-300x237.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 8.<br \/>\nj(x) = 0.75x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nm(x) = -2x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43813\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 9\" width=\"563\" height=\"502\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-9.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-9-300x267.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 10.<br \/>\nq(x) = &#8211;\\(\\frac{9}{2}\\)x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nk(x) = -0.2x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43814\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 11\" width=\"586\" height=\"499\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-11.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-11-300x255.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 12.<br \/>\np(x) = &#8211;\\(\\frac{2}{3}\\)x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 13\u201316, use a graphing calculator to graph the function. Compare the graph to the graph of y = \u22124x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 13.<br \/>\ny = 4x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43815\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 13\" width=\"573\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-13.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-13-300x125.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 14.<br \/>\ny = -0.4x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ny = -0.04x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43816\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 15\" width=\"582\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-15.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-15-300x125.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 16.<br \/>\ny = -0.004x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in graphing and comparing y = x<sup>2<\/sup> and y = 0.5x<sup>2<\/sup>.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-8.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 8\" width=\"326\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-8.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-8-300x201.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43817\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 17\" width=\"553\" height=\"404\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-17.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-17-300x219.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 18.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe arch support of a bridge can be modeled by y = -0.0012x<sup>2<\/sup>, where x and y are measured in feet. Find the height and width of the arch.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35955\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 9\" width=\"336\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-9.png 336w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-9-300x145.png 300w\" sizes=\"(max-width: 336px) 100vw, 336px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe breaking strength z (in pounds) of a manila rope can be modeled by z = 8900d<sup>2<\/sup>, where d is the diameter (in inches) of the rope.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-10.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 10\" width=\"156\" height=\"108\" \/><br \/>\na. Describe the domain and range of the function.<br \/>\nb. Graph the function using the domain in part (a).<br \/>\nc. A manila rope has four times the breaking strength of another manila rope. Does the stronger rope have four times the diameter? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43818\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 19\" width=\"572\" height=\"685\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-19.png 572w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-19-251x300.png 251w\" sizes=\"(max-width: 572px) 100vw, 572px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nDescribe the possible values of a.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 11\" width=\"256\" height=\"380\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-11.png 256w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-11-202x300.png 202w\" sizes=\"(max-width: 256px) 100vw, 256px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>ANALYZING GRAPHS<\/strong> In Exercises 21\u201323, use the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-12.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 12\" width=\"235\" height=\"145\" \/><br \/>\nQuestion 21.<br \/>\nWhen is each function increasing?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43819\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 21\" width=\"570\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-21.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-21-300x28.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 22.<br \/>\nWhen is each function decreasing?<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nWhich function could include the point (-2, 3)? Find the value of a when the graph passes through (-2, 3).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43820\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 23\" width=\"580\" height=\"339\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-23.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-23-300x175.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 24.<br \/>\n<strong>REASONING<\/strong><br \/>\nIs the x-intercept of the graph of y = x<sup>2<\/sup> always 0? Justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<strong>REASONING<\/strong><br \/>\nA parabola opens up and passes through (-4, 2) and (6, -3). How do you know that (-4, 2) is not the vertex?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43821\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-25.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 25\" width=\"571\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-25.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-25-300x61.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p><strong>ABSTRACT REASONING<\/strong> In Exercises 26\u201329, determine whether the statement is always, sometimes, or never true. Explain your reasoning.<br \/>\nQuestion 26.<br \/>\nThe graph of f(x) = x<sup>2<\/sup> is narrower than the graph of g(x) = x<sup>2<\/sup> when a &gt; 0.<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nThe graph of f(x) = x<sup>2<\/sup> is narrower than the graph of g(x) = x<sup>2<\/sup> when |a| &gt; 1.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43822\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 27\" width=\"582\" height=\"110\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-27.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-27-300x57.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 28.<br \/>\nThe graph of f(x) = x<sup>2<\/sup> is wider than the graph of g(x) = x<sup>2<\/sup> when 0 &lt; |a| &lt; 1.<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\nThe graph of f(x) = x<sup>2<\/sup> is wider than the graph of g(x) = dx<sup>2<\/sup> when |a | &gt; |d| .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43823\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 29\" width=\"580\" height=\"109\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-29.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-29-300x56.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nDraw the isosceles triangle shown. Divide each leg into eight congruent segments. Connect the highest point of one leg with the lowest point of the other leg. Then connect the second highest point of one leg to the second lowest point of the other leg. Continue this process. Write a quadratic equation whose graph models the shape that appears.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 13\" width=\"299\" height=\"153\" \/><br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nThe diagram shows the parabolic cross section of a swirling glass of water, where x and y are measured in centimeters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35960\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-14.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 14\" width=\"174\" height=\"338\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-14.png 174w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-14-154x300.png 154w\" sizes=\"(max-width: 174px) 100vw, 174px\" \/><br \/>\na. About how wide is the mouth of the glass?<br \/>\nb. Your friend claims that the rotational speed of the water would have to increase for the cross section to be modeled by y = 0.1x<sup>2<\/sup>. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43824\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-31.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 31\" width=\"574\" height=\"261\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-31.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-31-300x136.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Evaluate the expression when n = 3 and x = \u22122.<\/strong><br \/>\nQuestion 32.<br \/>\nn<sup>2<\/sup> + 5<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n3x<sup>2<\/sup> &#8211; 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43825\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-33.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 33\" width=\"218\" height=\"134\" \/><\/p>\n<p>Question 34.<br \/>\n-4n<sup>2<\/sup> + 11<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\nn + 2x<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43826\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.1-a-35.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.1 a 35\" width=\"235\" height=\"132\" \/><\/p>\n<h3><a id=\"Lesson_8.2_Graphing_f(x)_=_ax2_+_c\"><\/a>Lesson 8.2 Graphing f(x) = ax<sup>2<\/sup> + c<\/h3>\n<p><strong>Essential Question<\/strong> How does the value of c affect the graph of f(x) = -ax<sup>2<\/sup> + c?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Graphing y = ax<sup>2<\/sup> + c<br \/>\nWork with a partner. Sketch the graphs of the functions in the same coordinate plane. What do you notice?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 1\" width=\"496\" height=\"257\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-1.png 496w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-1-300x155.png 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Finding x-Intercepts of Graphs<br \/>\nWork with a partner. Graph each function. Find the x-intercepts of the graph. Explain how you found the x-intercepts.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35962\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 2\" width=\"497\" height=\"253\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-2.png 497w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-2-300x153.png 300w\" sizes=\"(max-width: 497px) 100vw, 497px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow does the value of c affect the graph of f(x) = ax<sup>2<\/sup> + c?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nUse a graphing calculator to verify your answers to Question 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35963\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 3\" width=\"226\" height=\"179\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nThe figure shows the graph of a quadratic function of the form y = ax<sup>2<\/sup> + c. Describe possible values of a and c. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35964\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-4.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 4\" width=\"203\" height=\"139\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 1.<br \/>\ng(x) = x<sup>2<\/sup> &#8211; 5<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nh(x) = x<sup>2<\/sup> + 3<br \/>\nAnswer:<\/p>\n<p><strong>Graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 3.<br \/>\ng(x) = 2x<sup>2<\/sup> &#8211; 5<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nh(x) = &#8211; \\(\\frac{1}{4}\\)x<sup>2<\/sup> + 4<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nLet f(x) = 3x<sup>2<\/sup> &#8211; 1 and g(x) = f (x) + 3.<br \/>\na. Describe the transformation from the graph of f to the graph of g. Then graph f and g in the same coordinate plane.<br \/>\nb. Write an equation that represents g in terms of x.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nExplain why only nonnegative values of t are used in Example 4.<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe egg is dropped from a height of 100 feet. After how many seconds does the egg hit the ground?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_f(x)_=_ax2_+_c_8.2_Exercises\"><\/a>Graphing f(x) = ax<sup>2<\/sup> + c 8.2 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nState the vertex and axis of symmetry of the graph of y = ax<sup>2<\/sup> + c.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43827\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 1\" width=\"554\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-1.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-1-300x34.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow does the graph of y = ax<sup>2<\/sup> + c compare to the graph of y = ax<sup>2<\/sup>?<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20136, graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 3.<br \/>\ng(x) = x<sup>2<\/sup> + 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43828\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-3.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 3\" width=\"620\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-3.png 620w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-3-300x240.png 300w\" sizes=\"(max-width: 620px) 100vw, 620px\" \/><\/p>\n<p>Question 4.<br \/>\nh(x) = x<sup>2<\/sup> + 8<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\np(x) = x<sup>2<\/sup> &#8211; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43829\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 5\" width=\"617\" height=\"510\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-5.png 617w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-5-300x248.png 300w\" sizes=\"(max-width: 617px) 100vw, 617px\" \/><\/p>\n<p>Question 6.<br \/>\nq(x) = x<sup>2<\/sup> &#8211; 1<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 7\u201312, graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 7.<br \/>\ng(x) = -x<sup>2<\/sup> + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43830\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 7\" width=\"581\" height=\"524\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-7.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-7-300x271.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 8.<br \/>\nh(x) = -x<sup>2<\/sup> &#8211; 7<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ns(x) = 2x<sup>2<\/sup> &#8211; 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43831\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 9\" width=\"584\" height=\"553\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-9.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-9-300x284.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 10.<br \/>\nt(x) = -3x<sup>2<\/sup> + 1<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\np(x) = &#8211; \\(\\frac{1}{3}\\)x<sup>2<\/sup> &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43832\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-11.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 11\" width=\"566\" height=\"634\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-11.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-11-268x300.png 268w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 12.<br \/>\nq(x) = \\(\\frac{1}{2}\\)x<sup>2<\/sup> + 6<br \/>\nAnswer:<\/p>\n<p>In Exercises 13\u201316, describe the transformation from the graph of f to the graph of g. Then graph f and g in the same coordinate plane. Write an equation that represents g in terms of x.<br \/>\nQuestion 13.<br \/>\nf(x) = 3x<sup>2<\/sup> + 4<br \/>\ng(x) = f(x) + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43833\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-13.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 13\" width=\"563\" height=\"647\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-13.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-13-261x300.png 261w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 14.<br \/>\nf(x) = \\(\\frac{1}{2}\\)x<sup>2<\/sup> + 1<br \/>\ng(x) = f(x) &#8211; 4<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nf(x) = &#8211; \\(\\frac{1}{4}\\)x<sup>2<\/sup> &#8211; 6<br \/>\ng(x) = f(x) &#8211; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43834\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-15.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 15\" width=\"570\" height=\"743\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-15.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-15-230x300.png 230w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 16.<br \/>\nf(x) = 4x<sup>2<\/sup> &#8211; 5<br \/>\ng(x) = f(x) + 7<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in comparing the graphs.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35966\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-5.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 5\" width=\"327\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-5.png 327w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-5-300x222.png 300w\" sizes=\"(max-width: 327px) 100vw, 327px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43835\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-17.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 17\" width=\"585\" height=\"86\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-17.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-17-300x44.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 18.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in graphing and comparing f(x) = x<sup>2<\/sup> and g(x) = x<sup>2<\/sup> &#8211; 10.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35967\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-6.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 6\" width=\"326\" height=\"255\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-6.png 326w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-6-300x235.png 300w\" sizes=\"(max-width: 326px) 100vw, 326px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 19\u201326, find the zeros of the function.<\/strong><br \/>\nQuestion 19.<br \/>\ny = x<sup>2<\/sup> &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43836\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-19.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 19\" width=\"557\" height=\"454\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-19.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-19-300x245.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 20.<br \/>\ny = x<sup>2<\/sup> &#8211; 36<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nf(x) = -x<sup>2<\/sup> + 25<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43837\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-21.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 21\" width=\"566\" height=\"443\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-21.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-21-300x235.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 22.<br \/>\nf(x) = -x<sup>2<\/sup> + 49<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nf(x) = 4x<sup>2<\/sup> &#8211; 16<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43838\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-23.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 23\" width=\"550\" height=\"440\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-23.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-23-300x240.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 24.<br \/>\nf(x) = 3x<sup>2<\/sup> &#8211; 27<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nf(x) = -12x<sup>2<\/sup> + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43839\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-25.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 25\" width=\"575\" height=\"481\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-25.png 575w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-25-300x251.png 300w\" sizes=\"(max-width: 575px) 100vw, 575px\" \/><\/p>\n<p>Question 26.<br \/>\nf(x) = -8x<sup>2<\/sup> + 98<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA water balloon is dropped from a height of 144 feet.<br \/>\na. After how many seconds does the water balloon hit the ground?<br \/>\nb. Suppose the initial height is adjusted by k feet. How does this affect part (a)?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43840\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-27.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 27\" width=\"563\" height=\"581\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-27.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-27-291x300.png 291w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe function y = -16x<sup>2<\/sup> + 36 represents the height y (in feet) of an apple x seconds after falling from a tree. Find and interpret the x- and y-intercepts.<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 29\u201332, sketch a parabola with the given characteristics.<\/strong><br \/>\nQuestion 29.<br \/>\nThe parabola opens up, and the vertex is (0, 3).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43841\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-29.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 29\" width=\"249\" height=\"270\" \/><\/p>\n<p>Question 30.<br \/>\nThe vertex is (0, 4), and one of the x-intercepts is 2.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\nThe related function is increasing when x &lt; 0, and the zeros are -1 and 1.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43842\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-31.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 31\" width=\"254\" height=\"279\" \/><\/p>\n<p>Question 32.<br \/>\nThe highest point on the parabola is (0, -5).<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>DRAWING CONCLUSIONS<\/strong><br \/>\nYou and your friend both drop a ball at the same time. The function h(x) = -16x<sup>2<\/sup> + 256 represents the height (in feet) of your ball after x seconds. The function g(x) = -16x<sup>2<\/sup> + 300 represents the height (in feet) of your friend\u2019s ball after x seconds.<br \/>\na. Write the function T(x) = h(x) &#8211; g(x). What does T(x) represent?<br \/>\nb. When your ball hits the ground, what is the height of your friend\u2019s ball? Use a graph to justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43843\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-33.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 33\" width=\"563\" height=\"646\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-33.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-33-261x300.png 261w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that in the equation y = ax<sup>2<\/sup> + c, the vertex changes when the value of a changes. Is your friend correct? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>MATHEMATICAL CONNECTIONS<\/strong><br \/>\nThe area A (in square feet) of a square patio is represented by A = x<sup>2<\/sup>, where x is the length of one side of the patio. You add 48 square feet to the patio, resulting in a total area of 192 square feet. What are the dimensions of the original patio? Use a graph to justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43844\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-35.1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 35.1\" width=\"581\" height=\"504\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-35.1.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-35.1-300x260.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43845\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-35.2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 35.2\" width=\"401\" height=\"349\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-35.2.png 401w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-35.2-300x261.png 300w\" sizes=\"(max-width: 401px) 100vw, 401px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph of f(x) = ax<sup>2<\/sup> + c is shown. Points A and B are the same distance from the vertex of the graph of f. Which point is closer to the vertex of the graph of f as c increases?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35968\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-7.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 7\" width=\"159\" height=\"154\" \/><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>REASONING<\/strong><br \/>\nDescribe two algebraic methods you can use to find the zeros of the function f(t) = -16t<sup>2<\/sup> + 400. Check your answer by graphing.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43846\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-37.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 37\" width=\"588\" height=\"114\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-37.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-37-300x58.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe paths of water from three different garden waterfalls are given below. Each function gives the height h (in feet) and the horizontal distance d (in feet) of the water.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35969\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-8.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 8\" width=\"133\" height=\"153\" \/><br \/>\nWaterfall 1 h = -3.1d<sup>2<\/sup> + 4.8<br \/>\nWaterfall 2 h = -3.5d<sup>2<\/sup> + 1.9<br \/>\nWaterfall 3 h = -1.1d<sup>2<\/sup> + 1.6<br \/>\na. Which waterfall drops water from the highest point?<br \/>\nb. Which waterfall follows the narrowest path?<br \/>\nc. Which waterfall sends water the farthest?<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>WRITING EQUATIONS<\/strong><br \/>\nTwo acorns fall to the ground from an oak tree. One falls 45 feet, while the other falls 32 feet.<br \/>\na. For each acorn, write an equation that represents the height h (in feet) as a function of the time t (in seconds).<br \/>\nb. Describe how the graphs of the two equations are related.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43847\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-39.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 39\" width=\"571\" height=\"283\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-39.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-39-300x149.png 300w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nOne of two classic problems in calculus is to find the area under a curve. Approximate the area of the region bounded by the parabola and the x-axis. Show your work.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35970\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 9\" width=\"158\" height=\"152\" \/><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nA cross section of the parabolic surface of the antenna shown can be modeled by y = 0.012x<sup>2<\/sup>, where x and y are measured in feet. The antenna is moved up so that the outer edges of the dish are 25 feet above x-axis. Where is the vertex of the cross section located? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35971\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-10.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 10\" width=\"197\" height=\"124\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43848\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-41.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 41\" width=\"581\" height=\"297\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-41.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-41-300x153.png 300w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Evaluate the expression when a = 4 and b = \u22123.<\/strong><br \/>\nQuestion 42.<br \/>\n\\(\\frac{a}{4b}\\)<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n&#8211;\\(\\frac{b}{2a}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43849\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-43.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 43\" width=\"213\" height=\"60\" \/><\/p>\n<p>Question 44.<br \/>\n\\(\\frac{a-b}{3 a+b}\\)<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n&#8211;\\(\\frac{b+2 a}{a b}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43850\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-45.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions 8.2 a 45\" width=\"535\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-45.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-8.2-a-45-300x35.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<h3><a id=\"Lesson_8.3_Graphing_f(x)_=_ax2_+_bx_+_c\"><\/a>Lesson 8.3 Graphing f(x) = ax<sup>2<\/sup> + bx + c<\/h3>\n<p><strong>Essential Question<\/strong> How can you find the vertex of the graph of f(x) = ax<sup>2<\/sup> + bx + c?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Comparing x-Intercepts with the Vertex<br \/>\nWork with a partner.<br \/>\na. Sketch the graphs of y = 2x<sup>2<\/sup> &#8211; 8x and y = 2x<sup>2<\/sup> &#8211; 8x + 6.<br \/>\nb. What do you notice about the x-coordinate of the vertex of each graph?<br \/>\nc. Use the graph of y = 2x<sup>2<\/sup> &#8211; 8x to find its x-intercepts. Verify your answer by solving 0 = 2x<sup>2<\/sup> &#8211; 8x.<br \/>\nd. Compare the value of the x-coordinate of the vertex with the values of the x-intercepts.<\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Finding x-Intercepts<br \/>\nWork with a partner.<br \/>\na. Solve 0 = ax<sup>2<\/sup> + bx for x by factoring.<br \/>\nb. What are the x-intercepts of the graph of y = ax<sup>2<\/sup> + bx?<br \/>\nc. Copy and complete the table to verify your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35972\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 1\" width=\"180\" height=\"113\" \/><\/p>\n<p><strong>EXPLORATION 3<\/strong><\/p>\n<p>Deductive Reasoning<br \/>\nWork with a partner. Complete the following logical argument.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 2\" width=\"661\" height=\"276\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-2.png 661w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-2-300x125.png 300w\" sizes=\"(max-width: 661px) 100vw, 661px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 4.<br \/>\nHow can you find the vertex of the graph of f(x) = ax<sup>2<\/sup> + bx + c?<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nWithout graphing, find the vertex of the graph of f(x) = x<sup>2<\/sup> &#8211; 4x + 3. Check your result by graphing.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Find (a) the axis of symmetry and (b) the vertex of the graph of the function.<\/strong><br \/>\nQuestion 1.<br \/>\nf(x) = 3x<sup>2<\/sup> &#8211; 2x<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ng(x) = x<sup>2<\/sup> + 6x + 5<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nh(x) = &#8211; \\(\\frac{1}{2}\\)x<sup>2<\/sup> + 7x &#8211; 4<br \/>\nAnswer:<\/p>\n<p><strong>Graph the function. Describe the domain and range.<\/strong><br \/>\nQuestion 4.<br \/>\nh(x) = 2x<sup>2<\/sup> + 4x + 1<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nk(x) = x<sup>2<\/sup> &#8211; 8x + 7<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\np(x) = -5x<sup>2<\/sup> &#8211; 10x &#8211; 2<br \/>\nAnswer:<\/p>\n<p><strong>Tell whether the function has a minimum value or a maximum value. Then find the value.<\/strong><br \/>\nQuestion 7.<br \/>\ng(x) = 8x<sup>2<\/sup> &#8211; 8x + 6<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nh(x) = &#8211; \\(\\frac{1}{4}\\)x<sup>2<\/sup> + 3x + 1<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nThe cables between the two towers of the Tacoma Narrows Bridge in Washington form a parabola that can be modeled by y = 0.00016x<sup>2<\/sup> &#8211; 0.46x + 507, where x and y are measured in feet. What is the height of the cable above the water at its lowest point?<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nWhich balloon is in the air longer? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nWhich balloon reaches its maximum height faster? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_f(x)_=_ax2_+_bx_+_c_8.3_Exercises\"><\/a>Graphing f(x) = ax<sup>2<\/sup> + bx + c 8.3 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nExplain how you can tell whether a quadratic function has a maximum value or a minimum value without graphing the function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43851\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 1\" width=\"587\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-1.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-1-300x44.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>DIFFERENT WORDS, SAME QUESTION<\/strong><br \/>\nConsider the quadratic function f(x) = -2x<sup>2<\/sup> + 8x + 24. Which is different? Find \u201cboth\u201d answers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35974\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 3\" width=\"679\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-3.png 679w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-3-300x53.png 300w\" sizes=\"(max-width: 679px) 100vw, 679px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20136, find the vertex, the axis of symmetry, and the y-intercept of the graph.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-4.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 4\" width=\"138\" height=\"132\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43852\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 3\" width=\"530\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-3.png 530w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-3-300x34.png 300w\" sizes=\"(max-width: 530px) 100vw, 530px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35976\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 5\" width=\"130\" height=\"131\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35977\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-6.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 6\" width=\"134\" height=\"130\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43853\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-5.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 5\" width=\"603\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-5.png 603w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-5-300x30.png 300w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 7\" width=\"134\" height=\"136\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 7\u201312, find (a) the axis of symmetry and (b) the vertex of the graph of the function.<\/strong><br \/>\nQuestion 7.<br \/>\nf(x) = 2x<sup>2<\/sup> &#8211; 4x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43854\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 7\" width=\"334\" height=\"299\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-7.png 334w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-7-300x269.png 300w\" sizes=\"(max-width: 334px) 100vw, 334px\" \/><\/p>\n<p>Question 8.<br \/>\ny = 3x<sup>2<\/sup> + 2x<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ny = -9x<sup>2<\/sup> &#8211; 18x &#8211; 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43855\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-9.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 9\" width=\"368\" height=\"338\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-9.png 368w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-9-300x276.png 300w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><\/p>\n<p>Question 10.<br \/>\nf(x) = -6x<sup>2<\/sup> + 24x &#8211; 20<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nf(x) = \\(\\frac{2}{5}\\)x<sup>2<\/sup> &#8211; 4x + 14<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43856\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-11.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 11\" width=\"418\" height=\"448\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-11.png 418w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-11-280x300.png 280w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p>Question 12.<br \/>\ny = &#8211; \\(\\frac{3}{4}\\) x<sup>2<\/sup> + 9x &#8211; 18<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 13\u201318, graph the function. Describe the domain and range.<\/strong><br \/>\nQuestion 13.<br \/>\nf(x) = 2x<sup>2<\/sup> + 12x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43857\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-13.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 13\" width=\"580\" height=\"713\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-13.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-13-244x300.png 244w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 14.<br \/>\ny = 4x<sup>2<\/sup> + 24x + 13<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ny = -8x<sup>2<\/sup> &#8211; 16x &#8211; 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43858\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-15.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 15\" width=\"581\" height=\"727\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-15.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-15-240x300.png 240w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><\/p>\n<p>Question 16.<br \/>\nf(x) = -5x<sup>2<\/sup> + 20x &#8211; 7<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\ny = \\(\\frac{2}{3}\\)x<sup>2<\/sup> &#8211; 6x + 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43859\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-17.1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 17.1\" width=\"418\" height=\"558\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-17.1.png 418w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-17.1-225x300.png 225w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43860\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-17.2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 17.2\" width=\"560\" height=\"368\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-17.2.png 560w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-17.2-300x197.png 300w\" sizes=\"(max-width: 560px) 100vw, 560px\" \/><\/p>\n<p>Question 18.<br \/>\nf(x) = &#8211; \\(\\frac{1}{2}\\)x<sup>2<\/sup> &#8211; 3x &#8211; 4<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding the axis of symmetry of the graph of y = 3x<sup>2<\/sup> &#8211; 12x + 11.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35979\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-8.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 8\" width=\"283\" height=\"93\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43861\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-19.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 19\" width=\"594\" height=\"157\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-19.png 594w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-19-300x79.png 300w\" sizes=\"(max-width: 594px) 100vw, 594px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in graphing the function f(x) = -x<sup>2<\/sup>+ 4x + 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35980\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-9.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 9\" width=\"337\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-9.png 337w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-9-300x157.png 300w\" sizes=\"(max-width: 337px) 100vw, 337px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 21\u201326, tell whether the function has a minimum value or a maximum value. Then find the value.<\/strong><br \/>\nQuestion 21.<br \/>\ny = 3x<sup>2<\/sup> &#8211; 18x + 15<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43862\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-21.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 21\" width=\"573\" height=\"325\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-21.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-21-300x170.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 22.<br \/>\nf(x) = -5x<sup>2<\/sup> + 10x + 7<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nf(x) = -4x<sup>2<\/sup> + 4x &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43863\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-23.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 23\" width=\"588\" height=\"389\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-23.png 588w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-23-300x198.png 300w\" sizes=\"(max-width: 588px) 100vw, 588px\" \/><\/p>\n<p>Question 24.<br \/>\ny = 2x<sup>2<\/sup> &#8211; 10x + 13<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\ny = &#8211; \\(\\frac{1}{2}\\)x<sup>2<\/sup> &#8211; 11x + 6<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43864\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-25.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 25\" width=\"554\" height=\"541\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-25.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-25-300x293.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 26.<br \/>\nf(x) = \\(\\frac{1}{5}\\)x<sup>2<\/sup> &#8211; 5x + 27<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe function shown represents the height h (in feet) of a firework t seconds after it is launched. The firework explodes at its highest point.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35981\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-10.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 10\" width=\"309\" height=\"181\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-10.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-10-300x176.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\na. When does the firework explode?<br \/>\nb. At what height does the firework explode?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43865\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-27.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 27\" width=\"506\" height=\"302\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-27.png 506w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-27-300x179.png 300w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe function h(t) = -16t<sup>2<\/sup> + 16t represents the height (in feet) of a horse t seconds after it jumps during a steeplechase.<br \/>\na. When does the horse reach its maximum height?<br \/>\nb. Can the horse clear a fence that is 3.5 feet tall? If so, by how much?<br \/>\nc. How long is the horse in the air?<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe cable between two towers of a suspension bridge can be modeled by the function shown, where x and y are measured in feet. The cable is at road level midway between the towers.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35982\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-11.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 11\" width=\"355\" height=\"176\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-11.png 355w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-11-300x149.png 300w\" sizes=\"(max-width: 355px) 100vw, 355px\" \/><br \/>\na. How far from each tower shown is the lowest point of the cable?<br \/>\nb. How high is the road above the water?<br \/>\nc. Describe the domain and range of the function shown.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43866\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-29.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 29\" width=\"598\" height=\"597\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-29.png 598w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-29-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-29-150x150.png 150w\" sizes=\"(max-width: 598px) 100vw, 598px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>REASONING<\/strong><br \/>\nFind the axis of symmetry of the graph of the equation y = ax<sup>2<\/sup> + bx + c when b = 0. Can you find the axis of symmetry when a = 0? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>ATTENDING TO PRECISION<\/strong><br \/>\nThe vertex of a parabola is (3, -1). One point on the parabola is (6, 8). Find another point on the parabola. Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43867\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-31.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 31\" width=\"566\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-31.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-31-300x74.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that it is possible to draw a parabola through any two points with different x-coordinates. Is your friend correct? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>USING TOOLS<\/strong> In Exercises 33\u201336, use the minimum or maximum feature of a graphing calculator to approximate the vertex of the graph of the function.<br \/>\nQuestion 33.<br \/>\ny = 0.5x<sup>2<\/sup> + \\(\\sqrt{2x}\\) x &#8211; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43868\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-33.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 33\" width=\"573\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-33.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-33-300x45.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 34.<br \/>\ny = -6.2x<sup>2<\/sup> + 4.8x &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\ny = -\u03c0x<sup>2<\/sup>+ 3x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43869\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-35.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 35\" width=\"583\" height=\"85\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-35.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-35-300x44.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 36.<br \/>\ny = 0.25x<sup>2<\/sup> &#8211; 5<sup>2\/3<\/sup>x + 2<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe opening of one aircraft hangar is a parabolic arch that can be modeled by the equation y = -0.006x<sup>2<\/sup>+ 1.5x, where x and y are measured in feet. The opening of a second aircraft hangar is shown in the graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35983\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-12.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 12\" width=\"233\" height=\"128\" \/><br \/>\na. Which aircraft hangar is taller?<br \/>\nb. Which aircraft hangar is wider?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43870\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-37.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 37\" width=\"582\" height=\"436\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-37.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-37-300x225.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nAn office supply store sells about 80 graphing calculators per month for $120 each. For each $6 decrease in price, the store expects to sell eight more calculators. The revenue from calculator sales is given by the function R(n) = (unit price)(units sold), or R(n) = (120 &#8211; 6n)(80 + 8n), where n is the number of $6 price decreases.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-13.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 13\" width=\"159\" height=\"241\" \/><br \/>\na. How much should the store charge to maximize monthly revenue?<br \/>\nb. Using a different revenue model, the store expects to sell five more calculators for each $4 decrease in price. Which revenue model results in a greater maximum monthly revenue? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>MATHEMATICAL CONNECTIONS<\/strong> In Exercises 39 and 40, (a) find the value of x that maximizes the area of the figure and (b) find the maximum area.<br \/>\nQuestion 39.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-14.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 14\" width=\"168\" height=\"118\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43871\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-39.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 39\" width=\"585\" height=\"652\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-39.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-39-269x300.png 269w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 40<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-15.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 15\" width=\"260\" height=\"102\" \/><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>WRITING<\/strong><br \/>\nCompare the graph of g(x) = x<sup>2<\/sup> + 4x + 1 with the graph of h(x) = x<sup>2<\/sup> &#8211; 4x + 1.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43872\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-41.1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 41.1\" width=\"639\" height=\"604\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-41.1.png 639w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-41.1-300x284.png 300w\" sizes=\"(max-width: 639px) 100vw, 639px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43873\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-41.2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 41.2\" width=\"622\" height=\"650\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-41.2.png 622w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-41.2-287x300.png 287w\" sizes=\"(max-width: 622px) 100vw, 622px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nDuring an archery competition, an archer shoots an arrow. The arrow follows the parabolic path shown, where x and y are measured in meters.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35987\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-16.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 16\" width=\"225\" height=\"154\" \/><br \/>\na. What is the initial height of the arrow?<br \/>\nb. Estimate the maximum height of the arrow.<br \/>\nc. How far does the arrow travel?<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nThe graph of a quadratic function passes through (3, 2), (4, 7), and (9, 2). Does the graph open up or down? Explain your reasoning.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43874\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-43.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 43\" width=\"565\" height=\"172\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-43.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-43-300x91.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 44.<br \/>\n<strong>REASONING<\/strong><br \/>\nFor a quadratic function f, what does f(-\\(\\frac{b}{2a}\\)) represent? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nWrite a function of the form y = ax<sup>2<\/sup> + bx whose graph contains the points (1, 6) and (3, 6).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43875\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-45.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 45\" width=\"579\" height=\"476\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-45.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-45-300x247.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 46.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nParabolas A and B contain the points shown. Identify characteristics of each parabola, if possible. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-17.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 17\" width=\"225\" height=\"145\" \/><br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nAt a basketball game, an air cannon launches T-shirts into the crowd. The function y = &#8211; \\(\\frac{1}{8}\\)x<sup>2<\/sup> + 4x represents the path of a T-shirt. The function 3y = 2x &#8211; 14 represents the height of the bleachers. In both functions, y represents vertical height (in feet) and x represents horizontal distance (in feet). At what height does the T-shirt land in the bleachers?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43876\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-47.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 47\" width=\"580\" height=\"454\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-47.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-47-300x235.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 48.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nOne of two classic problems in calculus is finding the slope of a tangent line to a curve. An example of a tangent line, which just touches the parabola at one point, is shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-18.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 18\" width=\"150\" height=\"119\" \/><br \/>\nApproximate the slope of the tangent line to the graph of y = x<sup>2<\/sup> at the point (1, 1). Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nThe owners of a dog shelter want to enclose a rectangular play area on the side of their building. They have k feet of fencing. What is the maximum area of the outside enclosure in terms of k? (Hint: Find the y-coordinate of the vertex of the graph of the area function.)<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-19.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 19\" width=\"240\" height=\"169\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43877\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-49.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 49\" width=\"555\" height=\"597\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-49.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-49-279x300.png 279w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Describe the transformation(s) from the graph of f(x) = |x| to the graph of the given function.<\/strong><br \/>\nQuestion 50.<br \/>\nq(x) = |x + 6|<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\nh(x) = -0.5|x|<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43878\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-51.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 51\" width=\"562\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-51.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-51-300x49.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 52.<br \/>\ng(x) = |x &#8211; 2| + 5<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\np(x) = 3|x + 1|<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43879\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-53.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 a 53\" width=\"574\" height=\"88\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-53.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-a-53-300x46.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><\/p>\n<h3><a id=\"Graphing_Quadratic_Functions_Study_Skills:_Learning_Visually\"><\/a>Graphing Quadratic Functions Study Skills: Learning Visually<\/h3>\n<p><strong>8.1\u2013 8.3 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-20.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 20\" width=\"604\" height=\"71\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-20.png 604w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-20-300x35.png 300w\" sizes=\"(max-width: 604px) 100vw, 604px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\nSection 8.1<br \/>\nCharacteristics of Quadratic Functions, p. 420<br \/>\nGraphing f(x) = ax<sup>2<\/sup> When a &gt; 0, p. 421<br \/>\nGraphing f (x) = ax<sup>2<\/sup>When a &lt; 0, p. 421<\/p>\n<p>Section 8.2<br \/>\nGraphing f(x) = ax<sup>2<\/sup> + c, p. 426<\/p>\n<p>Section 8.3<br \/>\nGraphing f(x) = ax<sup>2<\/sup> + bx + c, p. 432<br \/>\nMaximum and Minimum Values, p. 433<\/p>\n<p><strong>Mathematical Practices<\/strong><\/p>\n<p>Question 1.<br \/>\nExplain your plan for solving Exercise 18 on page 423.<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nHow does graphing a function in Exercise 27 on page 429 help you answer the questions?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nWhat definition and characteristics of the graph of a quadratic function did you use to answer Exercise 44 on page 438?<br \/>\nAnswer:<\/p>\n<p><strong>Study Skills: Learning Visually<\/strong><\/p>\n<ul>\n<li>Draw a picture of a word problem before writing a verbal model. You do not have to be an artist.<\/li>\n<li>When making a review card for a word problem, include a picture. This will help you recall the information while taking a test.<\/li>\n<li>Make sure your notes are visually neat for easy recall<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-21.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions 8.3 21\" width=\"363\" height=\"274\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-21.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-8.3-21-300x226.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><\/li>\n<\/ul>\n<h3><a id=\"Graphing_Quadratic_Functions_8.1_-_8.3_Quiz\"><\/a>Graphing Quadratic Functions 8.1 &#8211; 8.3 Quiz<\/h3>\n<p><strong>Identify characteristics of the quadratic function and its graph.<\/strong><br \/>\nQuestion 1.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-q-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions q 1\" width=\"188\" height=\"186\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-q-2.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions q 2\" width=\"188\" height=\"189\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-q-2.png 188w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-q-2-150x150.png 150w\" sizes=\"(max-width: 188px) 100vw, 188px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 3.<br \/>\nh(x) = -x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\np(x) = 2x<sup>2<\/sup> + 2<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nr(x) = 4x<sup>2<\/sup> &#8211; 16<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nb(x) = 8x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\ng(x) = \\(\\frac{2}{5}\\)x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nm(x) = &#8211; \\(\\frac{1}{2}\\)x<sup>2<\/sup> &#8211; 4<br \/>\nAnswer:<\/p>\n<p>Describe the transformation from the graph of f to the graph of g. Then graph f and g in the same coordinate plane. Write an equation that represents g in terms of x.<br \/>\nQuestion 9.<br \/>\nf(x) = 2x<sup>2<\/sup> + 1; g(x) = f(x) + 2<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nf(x) = -3x<sup>2<\/sup> + 12; g(x) = f(x) &#8211; 9<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nf(x) = \\(\\frac{1}{2}\\)x<sup>2<\/sup> &#8211; 2; g(x) = f(x) &#8211; 6<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nf(x) = 5x<sup>2<\/sup> &#8211; 3; g(x) = f(x) + 1<br \/>\nAnswer:<\/p>\n<p><strong>Graph the function. Describe the domain and range.<\/strong><br \/>\nQuestion 13.<br \/>\nf(x) = -4x<sup>2<\/sup> &#8211; 4x + 7<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nf(x) = 2x<sup>2<\/sup> + 12x + 5<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\ny = x<sup>2<\/sup> + 4x &#8211; 5<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\ny = -3x<sup>2<\/sup> + 6x + 9<br \/>\nAnswer:<\/p>\n<p><strong>Tell whether the function has a minimum value or a maximum value. Then find the value.<\/strong><br \/>\nQuestion 17.<br \/>\nf(x) = 5x<sup>2<\/sup> + 10x &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\nf(x) = &#8211; \\(\\frac{1}{2}\\)x<sup>2<\/sup> + 2x + 16<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\ny = -x<sup>2<\/sup> + 4x + 12<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\ny = 2x<sup>2<\/sup> + 8x + 3<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nThe distance y (in feet) that a coconut falls after t seconds is given by the function y = 16t<sup>2<\/sup>. Use a graph to determine how many seconds it takes for the coconut to fall 64 feet.<br \/>\nAnswer:<\/p>\n<p>Question 22.<br \/>\nThe function y = -16t<sup>2<\/sup> + 25 represents the height y (in feet) of a pinecone t seconds after falling from a tree.<br \/>\na. After how many seconds does the pinecone hit the ground?<br \/>\nb. A second pinecone falls from a height of 36 feet. Which pinecone hits the ground in the least amount of time? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nThe function shown models the height (in feet) of a softball t seconds after it is pitched in an underhand motion. Describe the domain and range. Find the maximum height of the softball.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-q-3.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions q 3\" width=\"247\" height=\"183\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_8.4_Graphing_f(x)_=_a(x_-_h)2_+_k\"><\/a>Lesson 8.4 Graphing f(x) = a(x &#8211; h)<sup>2<\/sup> + k<\/h3>\n<p><strong>Essential Question<\/strong> How can you describe the graph of f(x) = a(x &#8211; h)<sup>2<\/sup>?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Graphing y = a(x \u2212 h)<sup>2<\/sup> When h &gt; 0<br \/>\nWork with a partner. Sketch the graphs of the functions in the same coordinate plane. How does the value of h affect the graph of y = a(x &#8211; h)<sup>2<\/sup>?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 1\" width=\"506\" height=\"251\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-1.png 506w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-1-300x149.png 300w\" sizes=\"(max-width: 506px) 100vw, 506px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Graphing y = a(x \u2212 h)<sup>2<\/sup> When h &lt; 0<br \/>\nWork with a partner. Sketch the graphs of the functions in the same coordinate plane. How does the value of h affect the graph of y = a(x &#8211; h)<sup>2<\/sup>?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 2\" width=\"511\" height=\"254\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-2.png 511w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-2-300x149.png 300w\" sizes=\"(max-width: 511px) 100vw, 511px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you describe the graph of f(x) = a(x &#8211; h)<sup>2<\/sup>?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nWithout graphing, describe the graph of each function. Use a graphing calculator to check your answer.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 3\" width=\"226\" height=\"180\" \/><br \/>\na. y = (x &#8211; 3)<sup>2<\/sup><br \/>\nb. y = (x + 3)<sup>2<\/sup><br \/>\nc. y = -(x &#8211; 3)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Determine whether the function is even, odd, or neither.<\/strong><br \/>\nQuestion 1.<br \/>\nf(x) = 5x<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ng(x) = 2x<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nh(x) = 2x<sup>2<\/sup> + 3<br \/>\nAnswer:<\/p>\n<p><strong>Graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 4.<br \/>\ng(x) = 2(x + 5)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nh(x) = -(x &#8211; 2)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>Graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 6.<br \/>\ng(x) = 3(x &#8211; 1)<sup>2<\/sup> + 6<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nh(x) = \\(\\frac{1}{2}\\)(x + 4)<sup>2<\/sup> &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nConsider function g in Example 3. Graph f(x) = g(x) &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nThe vertex is (3, 6). Write and graph a quadratic function that models the path.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_f(x)_=_a(x_-_h)2_+_k_8.4_Exercises\"><\/a>Graphing f(x) = a(x &#8211; h)<sup>2<\/sup> + k 8.4 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nCompare the graph of an even function with the graph of an odd function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43880\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 1\" width=\"554\" height=\"91\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-1.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-1-300x49.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>OPEN-ENDED<\/strong><br \/>\nWrite a quadratic function whose graph has a vertex of (1, 2).<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>WRITING<\/strong><br \/>\nDescribe the transformation from the graph of f(x) = ax<sup>2<\/sup> to the graph of g(x) = a(x &#8211; h)<sup>2<\/sup> + k.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43881\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-3.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 3\" width=\"553\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-3.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-3-300x63.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich function does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-35999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-4.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 4\" width=\"605\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-4.png 605w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-4-300x19.png 300w\" sizes=\"(max-width: 605px) 100vw, 605px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u201312, determine whether the function is even, odd, or neither.<\/strong><br \/>\nQuestion 5.<br \/>\nf(x) = 4x + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43882\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-5.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 5\" width=\"585\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-5.png 585w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-5-300x98.png 300w\" sizes=\"(max-width: 585px) 100vw, 585px\" \/><\/p>\n<p>Question 6.<br \/>\ng(x) = 3x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nh(x) = 5<sup>x<\/sup> + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43883\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-7.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 7\" width=\"517\" height=\"200\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-7.png 517w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-7-300x116.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><\/p>\n<p>Question 8.<br \/>\nm(x) = 2x<sup>2<\/sup> &#8211; 7x<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\np(x) = -x<sup>2<\/sup> + 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43884\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-9.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 9\" width=\"415\" height=\"174\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-9.png 415w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-9-300x126.png 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/><\/p>\n<p>Question 10.<br \/>\nf(x) = &#8211; \\(\\frac{1}{2}\\)x<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nn(x) = 2x<sup>2<\/sup> &#8211; 7x + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43885\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-11.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 11\" width=\"570\" height=\"191\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-11.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-11-300x101.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 12.<br \/>\nr(x) = -6x<sup>2<\/sup> + 5<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 13\u201318, determine whether the function represented by the graph is even, odd, or neither.<\/strong><br \/>\nQuestion 13.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-5.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 5\" width=\"126\" height=\"132\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43886\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-13.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 13\" width=\"562\" height=\"38\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-13.png 562w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-13-300x20.png 300w\" sizes=\"(max-width: 562px) 100vw, 562px\" \/><\/p>\n<p>Question 14.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-6.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 6\" width=\"131\" height=\"133\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-7.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 7\" width=\"130\" height=\"129\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43887\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-15.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 15\" width=\"577\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-15.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-15-300x28.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-8.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 8\" width=\"131\" height=\"128\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-9.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 9\" width=\"134\" height=\"125\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43888\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-17.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 17\" width=\"567\" height=\"33\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-17.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-17-300x17.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-10.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 10\" width=\"138\" height=\"135\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 19\u201322, find the vertex and the axis of symmetry of the graph of the function.<\/strong><br \/>\nQuestion 19.<br \/>\nf(x) = 3(x + 1)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43889\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-19.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 19\" width=\"580\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-19.png 580w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-19-300x31.png 300w\" sizes=\"(max-width: 580px) 100vw, 580px\" \/><\/p>\n<p>Question 20.<br \/>\nf(x) = \\(\\frac{1}{4}\\)(x &#8211; 6)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\ny = &#8211; \\(\\frac{1}{8}\\)(x &#8211; 4)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43890\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-21.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 21\" width=\"555\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-21.png 555w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-21-300x35.png 300w\" sizes=\"(max-width: 555px) 100vw, 555px\" \/><\/p>\n<p>Question 22.<br \/>\ny = -5(x + 9)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 23\u201328, graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 23.<br \/>\ng(x) = 2(x + 3)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43891\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-23.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 23.1\" width=\"573\" height=\"593\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-23.1.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-23.1-290x300.png 290w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43892\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-23.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 23.2\" width=\"578\" height=\"173\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-23.2.png 578w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-23.2-300x90.png 300w\" sizes=\"(max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>Question 24.<br \/>\np(x) = 3(x &#8211; 1)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\nr(x) = \\(\\frac{1}{4}\\)(x + 10)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43893\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-25.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 25.1\" width=\"577\" height=\"589\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-25.1.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-25.1-294x300.png 294w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43894\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-25.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 25.2\" width=\"595\" height=\"177\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-25.2.png 595w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-25.2-300x89.png 300w\" sizes=\"(max-width: 595px) 100vw, 595px\" \/><\/p>\n<p>Question 26.<br \/>\nn(x) = \\(\\frac{1}{4}\\)(x &#8211; 6)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nd(x) = \\(\\frac{1}{5}\\)(x &#8211; 5)<sup>2<\/sup><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43895\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-27.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 27.1\" width=\"680\" height=\"557\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-27.1.png 680w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-27.1-300x246.png 300w\" sizes=\"(max-width: 680px) 100vw, 680px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43896\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-27.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 27.2\" width=\"690\" height=\"146\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-27.2.png 690w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-27.2-300x63.png 300w\" sizes=\"(max-width: 690px) 100vw, 690px\" \/><\/p>\n<p>Question 28.<br \/>\nq(x) = 6(x + 2)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in determining whether the function f(x) = x<sup>2<\/sup> + 3 is even, odd, or neither.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-11.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 11\" width=\"318\" height=\"143\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-11.png 318w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-11-300x135.png 300w\" sizes=\"(max-width: 318px) 100vw, 318px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43897\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-29.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 29.1\" width=\"469\" height=\"207\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-29.1.png 469w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-29.1-300x132.png 300w\" sizes=\"(max-width: 469px) 100vw, 469px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in finding the vertex of the graph of the function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-12.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 12\" width=\"321\" height=\"89\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-12.png 321w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-12-300x83.png 300w\" sizes=\"(max-width: 321px) 100vw, 321px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 31\u201334, find the vertex and the axis of symmetry of the graph of the function.<\/strong><br \/>\nQuestion 31.<br \/>\ny = -6(x + 4)<sup>2<\/sup> &#8211; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43898\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-31.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 31\" width=\"568\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-31.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-31-300x31.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 32.<br \/>\nf(x) = 3(x &#8211; 3)<sup>2<\/sup> + 6<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\nf(x) = -4(x + 3)<sup>2<\/sup> + 1<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43899\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-33.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 33\" width=\"564\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-33.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-33-300x33.png 300w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><\/p>\n<p>Question 34.<br \/>\ny = -(x &#8211; 6)<sup>2<\/sup> &#8211; 5<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 35\u201338, match the function with its graph.<\/strong><br \/>\nQuestion 35.<br \/>\ny = -(x + 1)<sup>2<\/sup> &#8211; 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43900\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-35.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 35\" width=\"567\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-35.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-35-300x31.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 36.<br \/>\ny = &#8211; \\(\\frac{1}{2}\\)(x &#8211; 1)<sup>2<\/sup> + 3<br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\ny = \\(\\frac{1}{3}\\)(x &#8211; 1)<sup>2<\/sup> + 3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43901\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-37.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 37\" width=\"563\" height=\"92\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-37.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-37-300x49.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 38.<br \/>\ny = 2(x + 1)<sup>2<\/sup> &#8211; 3<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-13.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 13\" width=\"328\" height=\"268\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-13.png 328w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-13-300x245.png 300w\" sizes=\"(max-width: 328px) 100vw, 328px\" \/><\/p>\n<p><strong>In Exercises 39\u201344, graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 39.<br \/>\nh(x) = (x &#8211; 2)<sup>2<\/sup> + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43902\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-39.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 39.1\" width=\"577\" height=\"564\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-39.1.png 577w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-39.1-300x293.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43903\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-39.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 39.2\" width=\"545\" height=\"121\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-39.2.png 545w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-39.2-300x67.png 300w\" sizes=\"(max-width: 545px) 100vw, 545px\" \/><\/p>\n<p>Question 40.<br \/>\ng(x) = (x + 1)<sup>2<\/sup> &#8211; 7<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\nr(x) = 4(x &#8211; 1)<sup>2<\/sup> &#8211; 5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43904\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-41.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 41.1\" width=\"581\" height=\"627\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-41.1.png 581w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-41.1-278x300.png 278w\" sizes=\"(max-width: 581px) 100vw, 581px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43905\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-41.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 41.2\" width=\"602\" height=\"148\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-41.2.png 602w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-41.2-300x74.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><\/p>\n<p>Question 42.<br \/>\nn(x) = -(x + 4)<sup>2<\/sup> + 2<br \/>\nAnswer:<\/p>\n<p>Question 43.<br \/>\ng(x) = &#8211; \\(\\frac{1}{3}\\)(x + 3)<sup>2<\/sup> &#8211; 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43906\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-43.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 43.1\" width=\"561\" height=\"643\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-43.1.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-43.1-262x300.png 262w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43907\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-43.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 43.2\" width=\"566\" height=\"203\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-43.2.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-43.2-300x108.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 44.<br \/>\nr(x) = \\(\\frac{1}{2}\\)(x &#8211; 2)<sup>2<\/sup> &#8211; 4<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 45\u201348, let f(x) = (x \u2212 2)<sup>2<\/sup> + 1. Match the function with its graph.<\/strong><br \/>\nQuestion 45.<br \/>\ng(x) = f(x &#8211; 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43908\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-45.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 45\" width=\"527\" height=\"139\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-45.png 527w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-45-300x79.png 300w\" sizes=\"(max-width: 527px) 100vw, 527px\" \/><\/p>\n<p>Question 46.<br \/>\nr(x) = f(x + 2)<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\nh(x) = f(x) + 2<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43909\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-47.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 47\" width=\"568\" height=\"140\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-47.png 568w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-47-300x74.png 300w\" sizes=\"(max-width: 568px) 100vw, 568px\" \/><\/p>\n<p>Question 48.<br \/>\np(x) = f(x) &#8211; 3<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-14.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 14\" width=\"339\" height=\"268\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-14.png 339w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-14-300x237.png 300w\" sizes=\"(max-width: 339px) 100vw, 339px\" \/><\/p>\n<p><strong>In Exercises 49\u201354, graph g.<\/strong><br \/>\nQuestion 49.<br \/>\nf(x) = 2(x &#8211; 1)<sup>2<\/sup> + 1; g(x) = f(x + 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43910\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-49.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 49.1\" width=\"574\" height=\"475\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-49.1.png 574w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-49.1-300x248.png 300w\" sizes=\"(max-width: 574px) 100vw, 574px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43911\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-49.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 49.2\" width=\"301\" height=\"243\" \/><\/p>\n<p>Question 50.<br \/>\nf(x) = -(x + 1)<sup>2<\/sup> + 2; g(x) = \\(\\frac{1}{2}\\)f(x)<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\nf(x) = -3(x + 5)<sup>2<\/sup> &#8211; 6; g(x) = 2f(x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43912\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-51.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 51.1\" width=\"579\" height=\"476\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-51.1.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-51.1-300x247.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43913\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-51.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 51.2\" width=\"263\" height=\"237\" \/><\/p>\n<p>Question 52.<br \/>\nf(x) = 5(x &#8211; 3)<sup>2<\/sup> &#8211; 1; g(x) = (x) &#8211; 6<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\nf(x) = (x + 3)<sup>2<\/sup> + 5; g(x) = f(x &#8211; 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43914\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-53.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 53\" width=\"587\" height=\"682\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-53.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-53-258x300.png 258w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><\/p>\n<p>Question 54.<br \/>\nf(x) = -2(x &#8211; 4)<sup>2<\/sup> &#8211; 8; g(x) = -f(x)<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe height (in meters) of a bird diving to catch a fish is represented by h(t) = 5(t &#8211; 2.5)<sup>2<\/sup>, where t is the number of seconds after beginning the dive.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-15.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 15\" width=\"143\" height=\"159\" \/><br \/>\na. Graph h.<br \/>\nb. Another bird\u2019s dive is represented by r(t) = 2h(t). Graph r.<br \/>\nc. Compare the graphs. Which bird starts its dive from a greater height? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43915\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-55.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 55.1\" width=\"650\" height=\"624\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-55.1.png 650w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-55.1-300x288.png 300w\" sizes=\"(max-width: 650px) 100vw, 650px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43916\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-55.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 55.2\" width=\"664\" height=\"592\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-55.2.png 664w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-55.2-300x267.png 300w\" sizes=\"(max-width: 664px) 100vw, 664px\" \/><\/p>\n<p>Question 56.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA kicker punts a football. The height (in yards) of the football is represented by f(x) = &#8211; \\(\\frac{1}{9}\\)(x &#8211; 30)<sup>2<\/sup> + 25, where x is the horizontal distance (in yards) from the kicker\u2019s goal line.<br \/>\na. Graph f. Describe the domain and range.<br \/>\nb. On the next possession, the kicker punts the football. The height of the football is represented by g(x) = f (x + 5). Graph g. Describe the domain and range.<br \/>\nc. Compare the graphs. On which possession does the kicker punt closer to his goal line? Explain.<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 57\u201362, write a quadratic function in vertex form whose graph has the given vertex and passes through the given point.<\/strong><br \/>\nQuestion 57.<br \/>\nvertex: (1, 2); passes through (3, 10)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43917\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-57.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 57\" width=\"537\" height=\"366\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-57.png 537w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-57-300x204.png 300w\" sizes=\"(max-width: 537px) 100vw, 537px\" \/><\/p>\n<p>Question 58.<br \/>\nvertex: (-3, 5); passes through (0, -14)<br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\nvertex: (-2, -4); passes through (-1, -6)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43918\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-59.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 59\" width=\"589\" height=\"307\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-59.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-59-300x156.png 300w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 60.<br \/>\nvertex: (1, 8); passes through (3, 12)<br \/>\nAnswer:<\/p>\n<p>Question 61.<br \/>\nvertex: (5, -2); passes through (7, 0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43919\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-61.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 61\" width=\"565\" height=\"414\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-61.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-61-300x220.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 62.<br \/>\nvertex: (-5, -1); passes through (-2, 2)<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA portion of a roller coaster track is in the shape of a parabola. Write and graph a quadratic function that models this portion of the roller coaster with a maximum height of 90 feet, represented by a vertex of (25, 90), passing through the point (50, 0).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-16.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 16\" width=\"251\" height=\"137\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43920\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-63.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 63.1\" width=\"579\" height=\"623\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-63.1.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-63.1-279x300.png 279w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43921\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-63.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 63.2\" width=\"523\" height=\"518\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-63.2.png 523w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-63.2-300x297.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-63.2-150x150.png 150w\" sizes=\"(max-width: 523px) 100vw, 523px\" \/><\/p>\n<p>Question 64.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA flare is launched from a boat and travels in a parabolic path until reaching the water. Write and graph a quadratic function that models the path of the are with a maximum height of 300 meters, represented by a vertex of (59, 300), landing in the water at the point (119, 0).<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 65\u201368, rewrite the quadratic function in vertex form.<\/strong><br \/>\nQuestion 65.<br \/>\ny = 2x)<sup>2<\/sup> &#8211; 8x + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43922\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-65.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 65\" width=\"557\" height=\"697\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-65.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-65-240x300.png 240w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 66.<br \/>\ny = 3x)<sup>2<\/sup> + 6x &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\nf(x) = -5x)<sup>2<\/sup> + 10x + 36<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43923\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-67.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 67\" width=\"589\" height=\"612\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-67.png 589w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-67-289x300.png 289w\" sizes=\"(max-width: 589px) 100vw, 589px\" \/><\/p>\n<p>Question 68.<br \/>\nf(x) = -x)<sup>2<\/sup> + 4x + 2<br \/>\nAnswer:<\/p>\n<p>Question 69.<br \/>\n<strong>REASONING<\/strong><br \/>\nCan a function be symmetric about the x-axis? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43924\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-69.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 69\" width=\"554\" height=\"53\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-69.png 554w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-69-300x29.png 300w\" sizes=\"(max-width: 554px) 100vw, 554px\" \/><\/p>\n<p>Question 70.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph of a quadratic function is shown. Determine which symbols to use to complete the vertex form of the quadratic function. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-17.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 17\" width=\"176\" height=\"194\" \/><br \/>\nAnswer:<\/p>\n<p>In Exercises 71\u201374, describe the transformation from the graph of f to the graph of h. Write an equation that represents h in terms of x.<br \/>\nQuestion 71.<br \/>\nf(x) = -(x + 1))<sup>2<\/sup> &#8211; 2<br \/>\nh(x) = f(x) + 4<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43925\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-71.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 71\" width=\"579\" height=\"260\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-71.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-71-300x135.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 72.<br \/>\nf(x) = 2(x &#8211; 1))<sup>2<\/sup> + 1<br \/>\nh(x) = f(x &#8211; 5)<br \/>\nAnswer:<\/p>\n<p>Question 73.<br \/>\nf(x) = 4(x &#8211; 2))<sup>2<\/sup> + 3<br \/>\nh(x) = 2f(x)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43926\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-73.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 73\" width=\"570\" height=\"259\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-73.png 570w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-73-300x136.png 300w\" sizes=\"(max-width: 570px) 100vw, 570px\" \/><\/p>\n<p>Question 74.<br \/>\nf(x) = -(x + 5))<sup>2<\/sup> &#8211; 6<br \/>\nh(x) = \\(\\frac{1}{3}\\)f(x)<br \/>\nAnswer:<\/p>\n<p>Question 75.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe graph of y = x<sup>2<\/sup> is translated 2 units right and 5 units down. Write an equation for the function in vertex form and in standard form. Describe advantages of writing the function in each form.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43927\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-75.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 75\" width=\"586\" height=\"412\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-75.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-75-300x211.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 76.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nWhich of the following are true? Justify your answers.<br \/>\na. Any constant multiple of an even function is even.<br \/>\nb. Any constant multiple of an odd function is odd.<br \/>\nc. The sum or difference of two even functions is even.<br \/>\nd. The sum or difference of two odd functions is odd.<br \/>\ne. The sum or difference of an even function and an odd function is odd.<br \/>\nAnswer:<\/p>\n<p>Question 77.<br \/>\n<strong>COMPARING FUNCTIONS<\/strong><br \/>\nA cross section of a birdbath can be modeled by y = \\(\\frac{1}{81}\\)(x &#8211; 18)<sup>2<\/sup> &#8211; 4, where x and y are measured in inches. The graph shows the cross section of another birdbath.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-18.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 18\" width=\"220\" height=\"166\" \/><br \/>\na. Which birdbath is deeper? Explain.<br \/>\nb. Which birdbath is wider? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43928\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-77.1.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 77.1\" width=\"571\" height=\"612\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-77.1.png 571w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-77.1-280x300.png 280w\" sizes=\"(max-width: 571px) 100vw, 571px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43929\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-77.2.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 77.2\" width=\"561\" height=\"507\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-77.2.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-77.2-300x271.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 78.<br \/>\n<strong>REASONING<\/strong><br \/>\nCompare the graphs of y = 2x<sup>2<\/sup> + 8x +8 and y = x<sup>2<\/sup> without graphing the functions. How can factoring help you compare the parabolas? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 79.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend says all absolute value functions are even because of their symmetry. Is your friend correct? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43930\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-79.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 79\" width=\"563\" height=\"84\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-79.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-79-300x45.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Solve the equation.<\/strong><br \/>\nQuestion 80.<br \/>\nx(x &#8211; 1) = 0<br \/>\nAnswer:<\/p>\n<p>Question 81.<br \/>\n(x + 3)(x &#8211; 8) = 0<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43931\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-81.png\" alt=\"Big Ideas Math Answer Key Algebra 1 Chapter 8 Graphing Quadratic Functions 8.4 a 81\" width=\"368\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-81.png 368w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answer-Key-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.4-a-81-300x136.png 300w\" sizes=\"(max-width: 368px) 100vw, 368px\" \/><\/p>\n<p>Question 82.<br \/>\n(3x &#8211; 9)(4x + 12) = 0<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_8.5_Using_Intercept_Form\"><\/a>Lesson 8.5 Using Intercept Form<\/h3>\n<p><strong>Essential Question<\/strong> What are some of the characteristics of the graph of f(x) = a(x &#8211; p)(x &#8211; q)?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Using Zeros to Write Functions<br \/>\nWork with a partner. Each graph represents a function of the form f(x) = (x &#8211; p)(x &#8211; q) or f(x) = -(x &#8211; p)(x &#8211; q). Write the function represented by each graph. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 1\" width=\"499\" height=\"591\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-1.png 499w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-1-253x300.png 253w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 2.<br \/>\nWhat are some of the characteristics of the graph of f(x) = a(x &#8211; p)(x &#8211; q)?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nConsider the graph of f(x) = a(x &#8211; p)(x &#8211; q).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 2\" width=\"227\" height=\"192\" \/><br \/>\na. Does changing the sign of a change the x-intercepts? Does changing the sign of a change the y-intercept? Explain your reasoning.<br \/>\nb. Does changing the value of p change the x-intercepts? Does changing the value of p change the y-intercept? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Graph the quadratic function. Label the vertex, axis of symmetry, and x-intercepts. Describe the domain and range of the function.<\/strong><br \/>\nQuestion 1.<br \/>\nf(x) = (x + 2)(x &#8211; 3)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ng(x) = -2(x &#8211; 4)(x + 1)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nh(x) = 4x<sup>2<\/sup> &#8211; 36<br \/>\nAnswer:<\/p>\n<p><strong>Find the zero(s) of the function.<\/strong><br \/>\nQuestion 4.<br \/>\nf(x) = (x &#8211; 6)(x &#8211; 1)<br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\ng(x) = 3x<sup>2<\/sup> &#8211; 12x + 12<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nh(x) = x(x<sup>2<\/sup> &#8211; 1)<br \/>\nAnswer:<\/p>\n<p><strong>Use zeros to graph the function.<\/strong><br \/>\nQuestion 7.<br \/>\nf(x) = (x &#8211; 1)(x &#8211; 4)<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\ng(x) = x<sup>2<\/sup> + x &#8211; 12<br \/>\nAnswer:<\/p>\n<p><strong>Write a quadratic function in standard form whose graph satisfies the given condition(s).<\/strong><br \/>\nQuestion 9.<br \/>\nx-intercepts: -1 and 1<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nvertex: (8, 8) 11. passes through (0, 0), (10, 0), and (4, 12)<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\npasses through (-5, 0), (4, 0), and (3, -16)<br \/>\nAnswer:<\/p>\n<p><strong>Use zeros to graph the function.<\/strong><br \/>\nQuestion 13.<br \/>\ng(x) = (x &#8211; 1)(x &#8211; 3)(x + 3)<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nh(x) = x<sup>3<\/sup> &#8211; 6x<sup>2<\/sup> + 5x<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nThe zeros of a cubic function are -3, -1, and 1. The graph of the function passes through the point (0, -3). Write the function.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Using_Intercept_Form_8.5_Exercises\"><\/a>Using Intercept Form 8.5 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 values p and q are __________ of the graph of the function f(x) = a(x &#8211; p)(x &#8211; q).<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43932\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 1\" width=\"519\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-1.png 519w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-1-300x35.png 300w\" sizes=\"(max-width: 519px) 100vw, 519px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nExplain how to find the maximum value or minimum value of a quadratic function when the function is given in intercept form.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 3\u20136, find the x-intercepts and axis of symmetry of the graph of the function.<\/strong><br \/>\nQuestion 3.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-3.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 3\" width=\"162\" height=\"176\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43933\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-3.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 3\" width=\"534\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-3.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-3-300x70.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 4.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-4.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 4\" width=\"171\" height=\"182\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nf(x) = -5(x + 7)(x &#8211; 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43934\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-5.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 5\" width=\"544\" height=\"124\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-5.png 544w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-5-300x68.png 300w\" sizes=\"(max-width: 544px) 100vw, 544px\" \/><\/p>\n<p>Question 6.<br \/>\ng(x) = \\(\\frac{2}{3}\\) x(x + 8)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 7\u201312, graph the quadratic function. Label the vertex, axis of symmetry, and x-intercepts. Describe the domain and range of the function.<\/strong><br \/>\nQuestion 7.<br \/>\nf(x) = (x + 4)(x + 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43935\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-7.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 7\" width=\"538\" height=\"699\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-7.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-7-231x300.png 231w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 8.<br \/>\ny = (x &#8211; 2)(x + 2)<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\ny = -(x + 6)(x &#8211; 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43936\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-9.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 9\" width=\"561\" height=\"612\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-9.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-9-275x300.png 275w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 10.<br \/>\nh(x) = -4(x &#8211; 7)(x &#8211; 3)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\ng(x) = 5(x + 1)(x + 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43937\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-11.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 11\" width=\"591\" height=\"718\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-11.png 591w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-11-247x300.png 247w\" sizes=\"(max-width: 591px) 100vw, 591px\" \/><\/p>\n<p>Question 12.<br \/>\ny = -2(x &#8211; 3)(x + 4)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 13\u201320, graph the quadratic function. Label the vertex, axis of symmetry, and x-intercepts. Describe the domain and range of the function.<\/strong><br \/>\nQuestion 13.<br \/>\ny = x<sup>2<\/sup> &#8211; 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43938\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-13.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 13\" width=\"559\" height=\"728\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-13.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-13-230x300.png 230w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 14.<br \/>\nf(x) = x<sup>2<\/sup> &#8211; 8x<br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nh(x) = -5x<sup>2<\/sup> + 5x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43939\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-15.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 15.1\" width=\"553\" height=\"481\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-15.1.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-15.1-300x261.png 300w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43940\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-15.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 15.2\" width=\"496\" height=\"321\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-15.2.png 496w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-15.2-300x194.png 300w\" sizes=\"(max-width: 496px) 100vw, 496px\" \/><\/p>\n<p>Question 16.<br \/>\ny = 3x<sup>2<\/sup> &#8211; 48<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nq(x) = x<sup>2<\/sup> + 9x + 14<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43941\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-17.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 17.1\" width=\"502\" height=\"429\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-17.1.png 502w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-17.1-300x256.png 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43942\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-17.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 17.2\" width=\"516\" height=\"322\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-17.2.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-17.2-300x187.png 300w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><\/p>\n<p>Question 18.<br \/>\np(x) = x<sup>2<\/sup> + 6x &#8211; 27<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\ny = 4x<sup>2<\/sup> &#8211; 36x + 32<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43943\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-19.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 19.1\" width=\"516\" height=\"511\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-19.1.png 516w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-19.1-300x297.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-19.1-150x150.png 150w\" sizes=\"(max-width: 516px) 100vw, 516px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43944\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-19.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 19.2\" width=\"505\" height=\"335\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-19.2.png 505w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-19.2-300x199.png 300w\" sizes=\"(max-width: 505px) 100vw, 505px\" \/><\/p>\n<p>Question 20.<br \/>\ny = -2x<sup>2<\/sup> &#8211; 4x + 30<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 21\u201330, find the zero(s) of the function.<\/strong><br \/>\nQuestion 21.<br \/>\ny = -2(x &#8211; 2)(x &#8211; 10)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43945\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-21.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 21\" width=\"378\" height=\"158\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-21.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-21-300x125.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p>Question 22.<br \/>\nf(x) = \\(\\frac{1}{3}\\)(x + 5)(x &#8211; 1)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\ng(x) = x<sup>2<\/sup> + 5x &#8211; 24<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43946\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-23.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 23\" width=\"378\" height=\"95\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-23.png 378w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-23-300x75.png 300w\" sizes=\"(max-width: 378px) 100vw, 378px\" \/><\/p>\n<p>Question 24.<br \/>\ny = x<sup>2<\/sup> &#8211; 17x + 52<br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\ny = 3x<sup>2<\/sup> &#8211; 15x &#8211; 42<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43947\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-25.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 25\" width=\"373\" height=\"125\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-25.png 373w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-25-300x101.png 300w\" sizes=\"(max-width: 373px) 100vw, 373px\" \/><\/p>\n<p>Question 26.<br \/>\ng(x) = -4x<sup>2<\/sup> &#8211; 8x &#8211; 4<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nf(x) = (x + 5)(x<sup>2<\/sup> &#8211; 4)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43948\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-27.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 27\" width=\"418\" height=\"129\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-27.png 418w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-27-300x93.png 300w\" sizes=\"(max-width: 418px) 100vw, 418px\" \/><\/p>\n<p>Question 28.<br \/>\nh(x) = (x<sup>2<\/sup> &#8211; 36)(x &#8211; 11)<br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\ny = x<sup>3<\/sup> &#8211; 49x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43949\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-29.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 29\" width=\"404\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-29.png 404w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-29-300x120.png 300w\" sizes=\"(max-width: 404px) 100vw, 404px\" \/><\/p>\n<p>Question 30.<br \/>\ny = x<sup>3<\/sup> &#8211; x<sup>2<\/sup> &#8211; 9x + 9<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 31\u201336, match the function with its graph.<\/strong><br \/>\nQuestion 31.<br \/>\ny = (x + 5)(x + 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43950\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-31.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 31\" width=\"586\" height=\"59\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-31.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-31-300x30.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 32.<br \/>\ny = (x + 5)(x &#8211; 3)<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\ny = (x &#8211; 5)(x + 3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43951\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-33.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 33\" width=\"561\" height=\"58\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-33.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-33-300x31.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 34.<br \/>\ny = (x &#8211; 5)(x &#8211; 3)<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\ny = (x + 5)(x &#8211; 5)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43952\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-35.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 35\" width=\"567\" height=\"60\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-35.png 567w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-35-300x32.png 300w\" sizes=\"(max-width: 567px) 100vw, 567px\" \/><\/p>\n<p>Question 36.<br \/>\ny = (x + 3)(x &#8211; 3)<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-5.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 5\" width=\"345\" height=\"473\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-5.png 345w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-5-219x300.png 219w\" sizes=\"(max-width: 345px) 100vw, 345px\" \/><\/p>\n<p><strong>In Exercises 37\u201342, use zeros to graph the function.<\/strong><br \/>\nQuestion 37.<br \/>\nf(x) = (x + 2)(x &#8211; 6)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43953\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-37.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 37\" width=\"557\" height=\"552\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-37.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-37-300x297.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-37-150x150.png 150w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 38.<br \/>\ng(x) = -3(x + 1)(x + 7)<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\ny = x<sup>2<\/sup> &#8211; 11x + 18<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43954\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-39.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 39\" width=\"495\" height=\"481\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-39.png 495w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-39-300x292.png 300w\" sizes=\"(max-width: 495px) 100vw, 495px\" \/><\/p>\n<p>Question 40.<br \/>\ny = x<sup>2<\/sup> &#8211; x &#8211; 30<br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\ny = -5x<sup>2<\/sup> &#8211; 10x + 40<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43955\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-41.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 41\" width=\"550\" height=\"516\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-41.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-41-300x281.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 42.<br \/>\nh(x) = 8x<sup>2<\/sup> &#8211; 8<br \/>\nAnswer:<\/p>\n<p><strong>ERROR ANALYSIS<\/strong> In Exercises 43 and 44, describe and correct the error in finding the zeros of the function.<br \/>\nQuestion 43.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36019\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-6.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 6\" width=\"286\" height=\"101\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43956\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-43.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 43\" width=\"540\" height=\"230\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-43.png 540w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-43-300x128.png 300w\" sizes=\"(max-width: 540px) 100vw, 540px\" \/><\/p>\n<p>Question 44.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36020\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-7.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 7\" width=\"281\" height=\"101\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 45\u201356, write a quadratic function in standard form whose graph satisfies the given condition(s).<\/strong><br \/>\nQuestion 45.<br \/>\nvertex: (7, -3)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43957\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-45.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 45\" width=\"458\" height=\"277\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-45.png 458w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-45-300x181.png 300w\" sizes=\"(max-width: 458px) 100vw, 458px\" \/><\/p>\n<p>Question 46.<br \/>\nvertex: (4, 8)<br \/>\nAnswer:<\/p>\n<p>Question 47.<br \/>\nx-intercepts: 1 and 9<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43958\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-47.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 47\" width=\"459\" height=\"239\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-47.png 459w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-47-300x156.png 300w\" sizes=\"(max-width: 459px) 100vw, 459px\" \/><\/p>\n<p>Question 48.<br \/>\nx-intercepts: -2 and -5<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\npasses through (-4, 0), (3, 0), and (2, -18)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43959\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-49.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 49\" width=\"466\" height=\"495\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-49.png 466w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-49-282x300.png 282w\" sizes=\"(max-width: 466px) 100vw, 466px\" \/><\/p>\n<p>Question 50.<br \/>\npasses through (-5, 0), (-1, 0), and (-4, 3)<br \/>\nAnswer:<\/p>\n<p>Question 51.<br \/>\npasses through (7, 0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43960\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-51.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 51\" width=\"403\" height=\"242\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-51.png 403w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-51-300x180.png 300w\" sizes=\"(max-width: 403px) 100vw, 403px\" \/><\/p>\n<p>Question 52.<br \/>\npasses through (0, 0) and (6, 0)<br \/>\nAnswer:<\/p>\n<p>Question 53.<br \/>\naxis of symmetry: x = -5<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43961\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-53.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 53\" width=\"472\" height=\"271\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-53.png 472w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-53-300x172.png 300w\" sizes=\"(max-width: 472px) 100vw, 472px\" \/><\/p>\n<p>Question 54.<br \/>\ny increases as x increases when x &lt; 4; y decreases as x increases when x &gt; 4.<br \/>\nAnswer:<\/p>\n<p>Question 55.<br \/>\nrange: y \u2265 -3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43962\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-55.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 55\" width=\"376\" height=\"206\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-55.png 376w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-55-300x164.png 300w\" sizes=\"(max-width: 376px) 100vw, 376px\" \/><\/p>\n<p>Question 56.<br \/>\nrange: y \u2264 10<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 57\u201360, write the quadratic function represented by the graph.<\/strong><br \/>\nQuestion 57.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36021\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-8.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 8\" width=\"138\" height=\"147\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43963\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-57.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 57\" width=\"478\" height=\"502\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-57.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-57-286x300.png 286w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/p>\n<p>Question 58.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36022\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-9.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 9\" width=\"154\" height=\"147\" \/><br \/>\nAnswer:<\/p>\n<p>Question 59.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36023\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-10.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 10\" width=\"146\" height=\"144\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43964\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-59.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 59\" width=\"478\" height=\"503\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-59.png 478w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-59-285x300.png 285w\" sizes=\"(max-width: 478px) 100vw, 478px\" \/><\/p>\n<p>Question 60.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36024\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-11.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 11\" width=\"146\" height=\"142\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 61\u201368, use zeros to graph the function.<\/strong><br \/>\nQuestion 61.<br \/>\ny = 5x(x + 2)(x &#8211; 6)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43965\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-61.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 61\" width=\"551\" height=\"476\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-61.png 551w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-61-300x259.png 300w\" sizes=\"(max-width: 551px) 100vw, 551px\" \/><\/p>\n<p>Question 62.<br \/>\nf(x) = -x(x + 9)(x + 3)<br \/>\nAnswer:<\/p>\n<p>Question 63.<br \/>\nh(x) = (x &#8211; 2)(x + 2)(x + 7)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43966\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-63.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 63\" width=\"489\" height=\"477\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-63.png 489w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-63-300x293.png 300w\" sizes=\"(max-width: 489px) 100vw, 489px\" \/><\/p>\n<p>Question 64.<br \/>\ny = (x + 1)(x &#8211; 5)(x &#8211; 4)<br \/>\nAnswer:<\/p>\n<p>Question 65.<br \/>\nf(x) = 3x<sup>3<\/sup> &#8211; 48x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43967\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-65.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 65\" width=\"553\" height=\"578\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-65.png 553w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-65-287x300.png 287w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<p>Question 66.<br \/>\ny = -2x<sup>3<\/sup> + 20x<sup>2<\/sup> &#8211; 50x<br \/>\nAnswer:<\/p>\n<p>Question 67.<br \/>\ny = -x<sup>3<\/sup> &#8211; 16x<sup>2<\/sup> &#8211; 28x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43968\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-67.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 67\" width=\"512\" height=\"560\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-67.png 512w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-67-274x300.png 274w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/p>\n<p>Question 68.<br \/>\ng(x) = 6x<sup>3<\/sup> + 30x<sup>2<\/sup> &#8211; 36x<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 69\u201372, write the cubic function represented by the graph.<\/strong><br \/>\nQuestion 69.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36025\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-12.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 12\" width=\"141\" height=\"155\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43969\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-69.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 69\" width=\"470\" height=\"497\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-69.png 470w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-69-284x300.png 284w\" sizes=\"(max-width: 470px) 100vw, 470px\" \/><\/p>\n<p>Question 70.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36026\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-13.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 13\" width=\"145\" height=\"159\" \/><br \/>\nAnswer:<\/p>\n<p>Question 71.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36027\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-14.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 14\" width=\"152\" height=\"160\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43970\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-71.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 71\" width=\"479\" height=\"536\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-71.png 479w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-71-268x300.png 268w\" sizes=\"(max-width: 479px) 100vw, 479px\" \/><\/p>\n<p>Question 72.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36028\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-15.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 15\" width=\"148\" height=\"162\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 73\u201376, write a cubic function whose graph satisfies the given condition(s).<\/strong><br \/>\nQuestion 73.<br \/>\nx-intercepts: -2, 3, and 8<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43971\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-73.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 73\" width=\"534\" height=\"351\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-73.png 534w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-73-300x197.png 300w\" sizes=\"(max-width: 534px) 100vw, 534px\" \/><\/p>\n<p>Question 74.<br \/>\nx-intercepts: -7, -5, and 0<br \/>\nAnswer:<\/p>\n<p>Question 75.<br \/>\npasses through (1, 0) and (7, 0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43972\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-75.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 75\" width=\"446\" height=\"318\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-75.png 446w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-75-300x214.png 300w\" sizes=\"(max-width: 446px) 100vw, 446px\" \/><\/p>\n<p>Question 76.<br \/>\npasses through (0, 6)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 77\u201380, all the zeros of a function are given. Use the zeros and the other point given to write a quadratic or cubic function represented by the table.<\/strong><br \/>\nQuestion 77.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36029\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-16.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 16\" width=\"110\" height=\"120\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43973\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-77.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 77\" width=\"433\" height=\"463\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-77.png 433w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-77-281x300.png 281w\" sizes=\"(max-width: 433px) 100vw, 433px\" \/><\/p>\n<p>Question 78.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36030\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-17.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 17\" width=\"114\" height=\"125\" \/><br \/>\nAnswer:<\/p>\n<p>Question 79.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36031\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-18.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 18\" width=\"112\" height=\"145\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43974\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-79.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 79\" width=\"503\" height=\"502\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-79.png 503w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-79-300x300.png 300w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-79-150x150.png 150w\" sizes=\"(max-width: 503px) 100vw, 503px\" \/><\/p>\n<p>Question 80.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36032\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-19.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 19\" width=\"119\" height=\"147\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 81\u201384, sketch a parabola that satisfies the given conditions.<\/strong><br \/>\nQuestion 81.<br \/>\nx-intercepts: -4 and 2; range: y \u2265 -3<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43975\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-81.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 81\" width=\"561\" height=\"384\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-81.png 561w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-81-300x205.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/p>\n<p>Question 82.<br \/>\naxis of symmetry: x = 6; passes through (4, 15)<br \/>\nAnswer:<\/p>\n<p>Question 83.<br \/>\nrange: y \u2264 5; passes through (0, 2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43976\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-83.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 83\" width=\"250\" height=\"276\" \/><\/p>\n<p>Question 84.<br \/>\nx-intercept: 6; y-intercept: 1; range: y \u2265 -4<br \/>\nAnswer:<\/p>\n<p>Question 85.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nSatellite dishes are shaped like parabolas to optimally receive signals. The cross section of a satellite dish can be modeled by the function shown, where x and y are measured in feet. The x-axis represents the top of the opening of the dish.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36033\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-20.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 20\" width=\"283\" height=\"332\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-20.png 283w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-20-256x300.png 256w\" sizes=\"(max-width: 283px) 100vw, 283px\" \/><br \/>\na. How wide is the satellite dish?<br \/>\nb. How deep is the satellite dish?<br \/>\nc. Write a quadratic function in standard form that models the cross section of a satellite dish that is 6 feet wide and 1.5 feet deep.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43977\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-85.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 85.1\" width=\"454\" height=\"613\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-85.1.png 454w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-85.1-222x300.png 222w\" sizes=\"(max-width: 454px) 100vw, 454px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43978\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-85.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 85.2\" width=\"507\" height=\"120\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-85.2.png 507w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-85.2-300x71.png 300w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/p>\n<p>Question 86.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA professional basketball player\u2019s shot is modeled by the function shown, where x and y are measured in feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36034\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-21.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 21\" width=\"246\" height=\"158\" \/><br \/>\na. Does the player make the shot? Explain.<br \/>\nb. The basketball player releases another shot from the point (13, 0) and makes the shot. The shot also passes through the point (10, 1.4). Write a quadratic function in standard form that models the path of the shot.<br \/>\nAnswer:<\/p>\n<p><strong>USING STRUCTURE<\/strong> In Exercises 87\u201390, match the function with its graph.<br \/>\nQuestion 87.<br \/>\ny = -x<sup>2<\/sup> + 5x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43979\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-87.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 87\" width=\"525\" height=\"146\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-87.png 525w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-87-300x83.png 300w\" sizes=\"(max-width: 525px) 100vw, 525px\" \/><\/p>\n<p>Question 88.<br \/>\ny = x<sup>2<\/sup> &#8211; x &#8211; 12<br \/>\nAnswer:<\/p>\n<p>Question 89.<br \/>\ny = x<sup>3<\/sup> &#8211; 2x<sup>2<\/sup> &#8211; 8x<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43980\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-89.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 89\" width=\"583\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-89.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-89-300x112.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 90.<br \/>\ny = x<sup>3<\/sup> &#8211; 4x<sup>2<\/sup> &#8211; 11x + 30<br \/>\nAnswer:<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-36035\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-22.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 22\" width=\"335\" height=\"276\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-22.png 335w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-22-300x247.png 300w\" sizes=\"(max-width: 335px) 100vw, 335px\" \/><\/p>\n<p>Question 91.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nWrite a quadratic function represented by the table, if possible. If not, explain why.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36036\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-23.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 23\" width=\"214\" height=\"73\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43981\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-91.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 91\" width=\"559\" height=\"167\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-91.png 559w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-91-300x90.png 300w\" sizes=\"(max-width: 559px) 100vw, 559px\" \/><\/p>\n<p>Question 92.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nThe graph shows the parabolic arch that supports the roof of a convention center, where x and y are measured in feet.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36037\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-24.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 24\" width=\"309\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-24.png 309w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-24-300x114.png 300w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><br \/>\na. The arch can be represented by a function of the form f(x) = a(x &#8211; p)(x &#8211; q). Estimate the values of p and q.<br \/>\nb. Estimate the width and height of the arch. Explain how you can use your height estimate to calculate a.<br \/>\nAnswer:<\/p>\n<p><strong>ANALYZING EQUATIONS<\/strong> In Exercises 93 and 94,<br \/>\n(a) rewrite the quadratic function in intercept form and<br \/>\n(b) graph the function using any method. Explain the method you used.<br \/>\nQuestion 93.<br \/>\nf(x) = -3(x + 1)<sup>2<\/sup> + 27<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43982\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-93.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 93.1\" width=\"425\" height=\"565\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-93.1.png 425w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-93.1-226x300.png 226w\" sizes=\"(max-width: 425px) 100vw, 425px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43983\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-93.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 93.2\" width=\"566\" height=\"112\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-93.2.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-93.2-300x59.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 94.<br \/>\ng(x) = 2(x &#8211; 1)<sup>2<\/sup> &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 95.<br \/>\n<strong>WRITING<\/strong><br \/>\nCan a quadratic function with exactly one real zero be written in intercept form? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43984\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-95.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 95\" width=\"602\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-95.png 602w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-95-300x64.png 300w\" sizes=\"(max-width: 602px) 100vw, 602px\" \/><\/p>\n<p>Question 96.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nYour friend claims that any quadratic function can be written in standard form and in vertex form. Is your friend correct? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 97.<br \/>\n<strong>PROBLEM SOLVING<\/strong><br \/>\nWrite the function represented by the graph in intercept form.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36038\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-25.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 25\" width=\"214\" height=\"193\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43985\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-97.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 97\" width=\"471\" height=\"334\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-97.png 471w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-97-300x213.png 300w\" sizes=\"(max-width: 471px) 100vw, 471px\" \/><\/p>\n<p>Question 98.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nSketch the graph of each function. Explain your procedure.<br \/>\na. f(x) = (x<sup>2<\/sup> &#8211; 1)(x<sup>2<\/sup> &#8211; 4)<br \/>\nb. g(x) = x(x<sup>2<\/sup> &#8211; 1)(x<sup>2<\/sup> &#8211; 4)<br \/>\nAnswer:<\/p>\n<p>Question 99.<br \/>\n<strong>REASONING<\/strong><br \/>\nLet k be a constant. Find the zeros of the function f(x) = kx<sup>2<\/sup> &#8211; k<sup>2<\/sup>x &#8211; 2k<sup>3<\/sup> in terms of k.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43986\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-99.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 99\" width=\"422\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-99.png 422w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-99-300x173.png 300w\" sizes=\"(max-width: 422px) 100vw, 422px\" \/><\/p>\n<p><strong>PROBLEM SOLVING<\/strong> In Exercises 100 and 101, write a system of two quadratic equations whose graphs intersect at the given points. Explain your reasoning.<br \/>\nQuestion 100.<br \/>\n(-4, 0) and (2, 0)<br \/>\nAnswer:<\/p>\n<p>Question 101.<br \/>\n(3, 6) and (7, 6)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43987\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-101.1.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 101.1\" width=\"521\" height=\"568\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-101.1.png 521w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-101.1-275x300.png 275w\" sizes=\"(max-width: 521px) 100vw, 521px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43988\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-101.2.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 101.2\" width=\"582\" height=\"409\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-101.2.png 582w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-101.2-300x211.png 300w\" sizes=\"(max-width: 582px) 100vw, 582px\" \/><\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p>The scatter plot shows the amounts x (in grams) of fat and the numbers y of calories in 12 burgers at a fast-food restaurant.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36039\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-26.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 26\" width=\"244\" height=\"240\" \/><br \/>\nQuestion 102.<br \/>\nHow many calories are in the burger that contains 12 grams of fat?<br \/>\nAnswer:<\/p>\n<p>Question 103.<br \/>\nHow many grams of fat are in the burger that contains 600 calories?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43989\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-103.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 103\" width=\"501\" height=\"87\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-103.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-103-300x52.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<p>Question 104.<br \/>\nWhat tends to happen to the number of calories as the number of grams of fat increases?<br \/>\nAnswer:<\/p>\n<p>Determine whether the sequence is arithmetic, geometric, or neither. Explain your reasoning.<br \/>\nQuestion 105.<br \/>\n3, 11, 21, 33, 47, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43990\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-105.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 105\" width=\"579\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-105.png 579w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-105-300x115.png 300w\" sizes=\"(max-width: 579px) 100vw, 579px\" \/><\/p>\n<p>Question 106.<br \/>\n-2, -6, -18, -54, . . .<br \/>\nAnswer:<\/p>\n<p>Question 107.<br \/>\n26, 18, 10, 2, -6, . . .<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43991\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-107.png\" alt=\"Big Ideas Math Answers Algebra 1 Chapter 8 Graphing Quadratic Functions 8.5 a 107\" width=\"573\" height=\"128\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-107.png 573w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Answers-Algebra-1-Chapter-8-Graphing-Quadratic-Functions-8.5-a-107-300x67.png 300w\" sizes=\"(max-width: 573px) 100vw, 573px\" \/><\/p>\n<p>Question 108.<br \/>\n4, 5, 9, 14, 23, . . .<br \/>\nAnswer:<\/p>\n<h3><a id=\"Lesson_8.6_Comparing_Linear,_Exponential,_and_Quadratic_Functions\"><\/a>Lesson 8.6 Comparing Linear, Exponential, and Quadratic Functions<\/h3>\n<p><strong>Essential Question<\/strong> How can you compare the growth rates of linear, exponential, and quadratic functions?<\/p>\n<p><strong>EXPLORATION 1<\/strong><\/p>\n<p>Comparing Speeds<br \/>\nWork with a partner. Three cars start traveling at the same time. The distance traveled in t minutes is y miles. Complete each table and sketch all three graphs in the same coordinate plane. Compare the speeds of the three cars. Which car has a constant speed? Which car is accelerating the most? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36042\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 1\" width=\"501\" height=\"202\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-1.png 501w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-1-300x121.png 300w\" sizes=\"(max-width: 501px) 100vw, 501px\" \/><\/p>\n<p><strong>EXPLORATION 2<\/strong><\/p>\n<p>Comparing Speeds<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36043\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 2\" width=\"219\" height=\"197\" \/><br \/>\nWork with a partner. Analyze the speeds of the three cars over the given time periods. The distance traveled in t minutes is y miles. Which car eventually overtakes the others?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36044\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 3\" width=\"500\" height=\"275\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-3.png 500w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-3-300x165.png 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/><\/p>\n<p><strong>Communicate Your Answer<\/strong><\/p>\n<p>Question 3.<br \/>\nHow can you compare the growth rates of linear, exponential, and quadratic functions?<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nWhich function has a growth rate that is eventually much greater than the growth rates of the other two functions? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress<\/strong><\/p>\n<p><strong>Plot the points. Tell whether the points appear to represent a linear, an exponential, or a quadratic function.<\/strong><br \/>\nQuestion 1.<br \/>\n(-1, 5), (2, -1), (0, -1), (3, 5), (1, -3)<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\n(-1, 2), (-2, 8), (-3, 32), (0, \\(\\frac{1}{2}\\)), (1, \\(\\frac{1}{8}\\))<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n(-3, 5), (0, -1), (2, -5), (-4, 7), (1, -3)<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nTell whether the table of values represents a linear, an exponential, or a quadratic function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36045\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-4.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 4\" width=\"222\" height=\"76\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nTell whether the table of values represents a linear, an exponential, or a quadratic function. Then write the function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36046\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 5\" width=\"223\" height=\"65\" \/><br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nCompare the websites in Example 4 by calculating and interpreting the average rates of change from Day 0 to Day 10.<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<strong>WHAT IF?<\/strong><br \/>\nTinyville\u2019s population increased by 8% each year. In what year were the populations about equal?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Comparing_Linear,_Exponential,_and_Quadratic_Functions_8.6_Exercises\"><\/a>Comparing Linear, Exponential, and Quadratic Functions 8.6 Exercises<\/h3>\n<p><strong>Vocabulary and Core Concept Check<\/strong><\/p>\n<p>Question 1.<br \/>\n<strong>WRITING<\/strong><br \/>\nName three types of functions that you can use to model data. Describe the equation and graph of each type of function.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43992\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 1\" width=\"592\" height=\"197\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-1.png 592w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-1-300x100.png 300w\" sizes=\"(max-width: 592px) 100vw, 592px\" \/><\/p>\n<p>Question 2.<br \/>\n<strong>WRITING<\/strong><br \/>\nHow can you decide whether to use a linear, an exponential, or a quadratic function to model a data set?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\n<strong>VOCABULARY<\/strong><br \/>\nDescribe how to find the average rate of change of a function y = f(x) between x = a and x = b.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43993\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-3.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 3\" width=\"517\" height=\"31\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-3.png 517w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-3-300x18.png 300w\" sizes=\"(max-width: 517px) 100vw, 517px\" \/><\/p>\n<p>Question 4.<br \/>\n<strong>WHICH ONE DOESN\u2019T BELONG?<\/strong><br \/>\nWhich graph does not belong with the other three? Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36047\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-6.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 6\" width=\"587\" height=\"129\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-6.png 587w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-6-300x66.png 300w\" sizes=\"(max-width: 587px) 100vw, 587px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Monitoring Progress and Modeling with Mathematics<\/strong><\/p>\n<p><strong>In Exercises 5\u20138, tell whether the points appear to represent a linear, an exponential, or a quadratic function.<\/strong><br \/>\nQuestion 5.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36048\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 7\" width=\"133\" height=\"154\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43994\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-5.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 5\" width=\"533\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-5.png 533w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-5-300x35.png 300w\" sizes=\"(max-width: 533px) 100vw, 533px\" \/><\/p>\n<p>Question 6.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36049\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-8.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 8\" width=\"134\" height=\"156\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36050\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 9\" width=\"135\" height=\"159\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43995\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-7.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 7\" width=\"576\" height=\"57\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-7.png 576w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-7-300x30.png 300w\" sizes=\"(max-width: 576px) 100vw, 576px\" \/><\/p>\n<p>Question 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36051\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-10.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 10\" width=\"143\" height=\"160\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 9\u201314, plot the points. Tell whether the points appear to represent a linear, an exponential, or a quadratic function.<\/strong><br \/>\nQuestion 9.<br \/>\n(-2, -1), (-1, 0), (1, 2), (2, 3), (0, 1)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43996\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-9.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 9\" width=\"563\" height=\"312\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-9.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-9-300x166.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 10.<br \/>\n( 0, \\(\\frac{1}{4}\\)), (1, 1), (2, 4), (3, 16), (-1, \\(\\frac{1}{16}\\))<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\n(0, -3), (1, 0), (2, 9), (-2, 9), (-1, 0)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43997\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 11\" width=\"535\" height=\"298\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-11.png 535w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-11-300x167.png 300w\" sizes=\"(max-width: 535px) 100vw, 535px\" \/><\/p>\n<p>Question 12.<br \/>\n(-1, -3), (-3, 5), (0, -1), (1, 5), (2, 15)<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\n(-4, -4), (-2, -3.4), (0, -), (2, -2.6), (4, -2)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43998\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 13\" width=\"557\" height=\"302\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-13.png 557w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-13-300x163.png 300w\" sizes=\"(max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>Question 14.<br \/>\n(0, 8), (-4, 0.25), (-3, 0.4), (-2, 1), (-1, 3)<br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 15\u201318, tell whether the table of values represents a linear, an exponential, or a quadratic function.<\/strong><br \/>\nQuestion 15.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36052\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-11.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 11\" width=\"271\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-43999\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 15\" width=\"538\" height=\"218\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-15.png 538w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-15-300x122.png 300w\" sizes=\"(max-width: 538px) 100vw, 538px\" \/><\/p>\n<p>Question 16.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36053\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-12.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 12\" width=\"274\" height=\"66\" \/><br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36054\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-13.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 13\" width=\"272\" height=\"62\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44000\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 17\" width=\"523\" height=\"221\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-17.png 523w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-17-300x127.png 300w\" sizes=\"(max-width: 523px) 100vw, 523px\" \/><\/p>\n<p>Question 18.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36055\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-14.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 14\" width=\"276\" height=\"68\" \/><br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA student takes a subway to a public library. The table shows the distances d (in miles) the student travels in t minutes. Let the time t represent the independent variable. Tell whether the data can be modeled by a linear, an exponential, or a quadratic function. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36056\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-15.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 15\" width=\"330\" height=\"63\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-15.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-15-300x57.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44001\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 19\" width=\"543\" height=\"271\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-19.png 543w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-19-300x150.png 300w\" sizes=\"(max-width: 543px) 100vw, 543px\" \/><\/p>\n<p>Question 20.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nA store sells custom circular rugs. The table shows the costs c (in dollars) of rugs that have diameters of d feet. Let the diameter d represent the independent variable. Tell whether the data can be modeled by a linear, an exponential, or a quadratic function. Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36057\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-16.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 16\" width=\"330\" height=\"220\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-16.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-16-300x200.png 300w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>In Exercises 21\u201326, tell whether the data represent a linear, an exponential, or a quadratic function. Then write the function.<\/strong><br \/>\nQuestion 21.<br \/>\n(-2, 8), (-1, 0), (0, -4), (1, -4), (2, 0), (3, 8)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44002\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 21\" width=\"565\" height=\"757\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-21.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-21-224x300.png 224w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 22.<br \/>\n(-3, 8), (-2, 4), (-1, 2), (0, 1), (1, 0.5)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36058\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-17.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 17\" width=\"271\" height=\"64\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44003\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 23\" width=\"565\" height=\"395\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-23.png 565w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-23-300x210.png 300w\" sizes=\"(max-width: 565px) 100vw, 565px\" \/><\/p>\n<p>Question 24.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36059\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-18.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 18\" width=\"270\" height=\"61\" \/><br \/>\nAnswer:<\/p>\n<p>Question 25.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36060\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-19.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 19\" width=\"160\" height=\"153\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44004\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-25.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 25\" width=\"566\" height=\"522\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-25.png 566w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-25-300x277.png 300w\" sizes=\"(max-width: 566px) 100vw, 566px\" \/><\/p>\n<p>Question 26.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36061\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-20.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 20\" width=\"164\" height=\"157\" \/><br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in determining whether the table represents a linear, an exponential, or a quadratic function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36062\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-21.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 21\" width=\"324\" height=\"204\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-21.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-21-300x189.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44005\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 27\" width=\"536\" height=\"273\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-27.png 536w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-27-300x153.png 300w\" sizes=\"(max-width: 536px) 100vw, 536px\" \/><\/p>\n<p>Question 28.<br \/>\n<strong>ERROR ANALYSIS<\/strong><br \/>\nDescribe and correct the error in writing the function represented by the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36063\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-22.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 22\" width=\"330\" height=\"379\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-22.png 330w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-22-261x300.png 261w\" sizes=\"(max-width: 330px) 100vw, 330px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 29.<br \/>\n<strong>REASONING<\/strong><br \/>\nThe table shows the numbers of people attending the first five football games at a high school.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36064\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-23.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 23\" width=\"324\" height=\"65\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-23.png 324w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-23-300x60.png 300w\" sizes=\"(max-width: 324px) 100vw, 324px\" \/><br \/>\na. Plot the points. Let the game g represent the independent variable.<br \/>\nb. Can a linear, an exponential, or a quadratic function represent this situation? Explain.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44006\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 29\" width=\"550\" height=\"436\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-29.png 550w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-29-300x238.png 300w\" sizes=\"(max-width: 550px) 100vw, 550px\" \/><\/p>\n<p>Question 30.<br \/>\n<strong>MODELING WITH MATHEMATICS<\/strong><br \/>\nThe table shows the breathing rates y (in liters of air per minute) of a cyclist traveling at different speeds x (in miles per hour).<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36065\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-24.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 24\" width=\"322\" height=\"236\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-24.png 322w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-24-300x220.png 300w\" sizes=\"(max-width: 322px) 100vw, 322px\" \/><br \/>\na. Plot the points. Let the speed x represent the independent variable. Then determine the type of function that best represents this situation.<br \/>\nb. Write a function that models the data.<br \/>\nc. Find the breathing rate of a cyclist traveling 18 miles per hour. Round your answer to the nearest tenth.<br \/>\nAnswer:<\/p>\n<p>Question 31.<br \/>\n<strong>ANALYZING RATES OF CHANGE<\/strong><br \/>\nThe function f(t) = -16t<sup>2<\/sup> + 48t + 3 represents the height (in feet) of a volleyball t seconds after it is hit into the air.<br \/>\na. Copy and complete the table.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36066\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-25.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 25\" width=\"312\" height=\"62\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-25.png 312w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-25-300x60.png 300w\" sizes=\"(max-width: 312px) 100vw, 312px\" \/><br \/>\nb. Plot the ordered pairs and draw a smooth curve through the points.<br \/>\nc. Describe where the function is increasing and decreasing.<br \/>\nd. Find the average rate of change for each 0.5-second interval in the table. What do you notice about the average rates of change when the function is increasing? decreasing?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44007\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-31.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 31.1\" width=\"563\" height=\"487\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-31.1.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-31.1-300x260.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44008\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-31.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 31.2\" width=\"563\" height=\"278\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-31.2.png 563w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-31.2-300x148.png 300w\" sizes=\"(max-width: 563px) 100vw, 563px\" \/><\/p>\n<p>Question 32.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nThe population of Town A in 1970 was 3000. The population of Town A increased by 20% every decade. Let x represent the number of decades since 1970. The graph shows the population of Town B.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36067\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-26.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 26\" width=\"162\" height=\"213\" \/><br \/>\na. Compare the populations of the towns by calculating and interpreting the average rates of change from 1990 to 2010.<br \/>\nb. Predict which town will have a greater population after 2020. Explain.<br \/>\nAnswer:<\/p>\n<p>Question 33.<br \/>\n<strong>ANALYZING RELATIONSHIPS<\/strong><br \/>\nThree organizations are collecting donations for a cause. Organization A begins with one donation, and the number of donations quadruples each hour. The table shows the numbers of donations collected by Organization B. The graph shows the numbers of donations collected by Organization C.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36068\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-27.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 27\" width=\"363\" height=\"243\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-27.png 363w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-27-300x201.png 300w\" sizes=\"(max-width: 363px) 100vw, 363px\" \/><br \/>\na. What type of function represents the numbers of donations collected by Organization A? B? C?<br \/>\nb. Find the average rates of change of each function for each 1-hour interval from t = 0 to t = 6.<br \/>\nc. For which function does the average rate of change increase most quickly? What does this tell you about the numbers of donations collected by the three organizations?<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44009\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-33.1.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 33.1\" width=\"564\" height=\"620\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-33.1.png 564w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-33.1-273x300.png 273w\" sizes=\"(max-width: 564px) 100vw, 564px\" \/><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44010\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-33.2.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 33.2\" width=\"549\" height=\"628\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-33.2.png 549w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-33.2-262x300.png 262w\" sizes=\"(max-width: 549px) 100vw, 549px\" \/><\/p>\n<p>Question 34.<br \/>\n<strong>COMPARING FUNCTIONS<\/strong><br \/>\nThe room expenses for two different resorts are shown.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36069\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-28.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 28\" width=\"331\" height=\"189\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-28.png 331w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-28-300x171.png 300w\" sizes=\"(max-width: 331px) 100vw, 331px\" \/><br \/>\na. For what length of vacation does each resort cost about the same?<br \/>\nb. Suppose Blue Water Resort charges $1450 for the first three nights and $105 for each additional night. Would Sea Breeze Resort ever be more expensive than Blue Water Resort? Explain.<br \/>\nc. Suppose Sea Breeze Resort charges $1200 for the first three nights. The charge increases 10% for each additional night. Would Blue Water Resort ever be more expensive than Sea Breeze Resort? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 35.<br \/>\n<strong>REASONING<\/strong><br \/>\nExplain why the average rate of change of a linear function is constant and the average rate of change of a quadratic or exponential function is not constant.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44011\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-35.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 35\" width=\"583\" height=\"222\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-35.png 583w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-35-300x114.png 300w\" sizes=\"(max-width: 583px) 100vw, 583px\" \/><\/p>\n<p>Question 36.<br \/>\n<strong>HOW DO YOU SEE IT?<\/strong><br \/>\nMatch each graph with its function. Explain your reasoning.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36070\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-29.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 29\" width=\"325\" height=\"357\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-29.png 325w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-29-273x300.png 273w\" sizes=\"(max-width: 325px) 100vw, 325px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 37.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIn the ordered pairs below, the y-values are given in terms of n. Tell whether the ordered pairs represent a linear, an exponential, or a quadratic function. Explain.<br \/>\n(1, 3n &#8211; 1), (2, 10n + 2), (3, 26n),<br \/>\n(4, 51n &#8211; 7), (5, 85n &#8211; 19)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44012\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-37.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 37\" width=\"569\" height=\"245\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-37.png 569w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-37-300x129.png 300w\" sizes=\"(max-width: 569px) 100vw, 569px\" \/><\/p>\n<p>Question 38.<br \/>\n<strong>USING STRUCTURE<\/strong><br \/>\nWrite a function that has constant second differences of 3.<br \/>\nAnswer:<\/p>\n<p>Question 39.<br \/>\n<strong>CRITICAL THINKING<\/strong><br \/>\nIs the graph of a set of points enough to determine whether the points represent a linear, an exponential, or a quadratic function? Justify your answer.<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44013\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-39.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 39\" width=\"584\" height=\"117\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-39.png 584w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-39-300x60.png 300w\" sizes=\"(max-width: 584px) 100vw, 584px\" \/><\/p>\n<p>Question 40.<br \/>\n<strong>THOUGHT PROVOKING<\/strong><br \/>\nFind four different patterns in the figure. Determine whether each pattern represents a linear, an exponential, or a quadratic function. Write a model for each pattern.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36071\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-30.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 30\" width=\"288\" height=\"98\" \/><br \/>\nAnswer:<\/p>\n<p>Question 41.<br \/>\n<strong>MAKING AN ARGUMENT<\/strong><br \/>\nFunction p is an exponential function and function q is a quadratic function. Your friend says that after about x = 3, function q will always have a greater y-value than function p. Is your friend correct? Explain.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36072\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-31.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 31\" width=\"164\" height=\"164\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-31.png 164w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-31-150x150.png 150w\" sizes=\"(max-width: 164px) 100vw, 164px\" \/><br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44014\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-41.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 41\" width=\"586\" height=\"115\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-41.png 586w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-41-300x59.png 300w\" sizes=\"(max-width: 586px) 100vw, 586px\" \/><\/p>\n<p>Question 42.<br \/>\n<strong>USING TOOLS<\/strong><br \/>\nThe table shows the amount a (in billions of dollars) United States residents spent on pets or pet-related products and services each year for a 5-year period. Let the year x represent the independent variable. Using technology, find a function that models the data. How did you choose the model? Predict how much residents will spend on pets or pet-related products and services in Year 7.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36073\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-32.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 32\" width=\"306\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-32.png 306w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-32-300x65.png 300w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Maintaining Mathematical Proficiency<\/strong><\/p>\n<p><strong>Evaluate the expression.<\/strong><br \/>\nQuestion 43.<br \/>\n\\(\\sqrt{121}\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44015\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-43.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 43\" width=\"177\" height=\"66\" \/><\/p>\n<p>Question 44.<br \/>\n\\(\\sqrt [ 3 ]{ 125 }\\)<br \/>\nAnswer:<\/p>\n<p>Question 45.<br \/>\n\\(\\sqrt [ 3 ]{ 512 }\\)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44016\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-45.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 45\" width=\"206\" height=\"73\" \/><\/p>\n<p>Question 46.<br \/>\n\\(\\sqrt [ 5 ]{ 243 }\\)<br \/>\nAnswer:<\/p>\n<p><strong>Find the product.<\/strong><br \/>\nQuestion 47.<br \/>\n(x + 8)(x &#8211; 8)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44017\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-47.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 47\" width=\"258\" height=\"71\" \/><\/p>\n<p>Question 48.<br \/>\n(4y + 2)(4y &#8211; 2)<br \/>\nAnswer:<\/p>\n<p>Question 49.<br \/>\n(3a &#8211; 5b)(3a + 5b)<br \/>\nAnswer:<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-44018\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-49.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 a 49\" width=\"347\" height=\"61\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-49.png 347w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-a-49-300x53.png 300w\" sizes=\"(max-width: 347px) 100vw, 347px\" \/><\/p>\n<p>Question 50.<br \/>\n(-2r + 6s)(-2r &#8211; 6s)<br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_Quadratic_Functions_Performance_Task:_Asteroid_Aim\"><\/a>Graphing Quadratic Functions Performance Task: Asteroid Aim<\/h3>\n<p><strong>8.4\u20138.6 What Did You Learn?<\/strong><\/p>\n<p><strong>Core Vocabulary<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36074\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-33.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 33\" width=\"656\" height=\"51\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-33.png 656w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-33-300x23.png 300w\" sizes=\"(max-width: 656px) 100vw, 656px\" \/><\/p>\n<p><strong>Core Concepts<\/strong><br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36075\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-34.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 34\" width=\"673\" height=\"284\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-34.png 673w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-34-300x127.png 300w\" sizes=\"(max-width: 673px) 100vw, 673px\" \/><\/p>\n<p><strong>Mathematical Practices<\/strong><\/p>\n<p>Question 1.<br \/>\nHow can you use technology to confirm your answer in Exercise 64 on page 448?<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nHow did you use the structure of the equation in Exercise 85 on page 457 to solve the problem?<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nDescribe why your answer makes sense considering the context of the data in Exercise 20 on page 466.<br \/>\nAnswer:<\/p>\n<p><strong>Performance Task: Asteroid Aim<\/strong><\/p>\n<p>Apps take a long time to design and program. One app in development is a game in which players shoot lasers at asteroids. They score points based on the number of hits per shot. The designer wants your feedback. Do you think students will like the game and want to play it? What changes would improve it?<br \/>\nTo explore the answers to this question and more, go to<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36076\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-35.png\" alt=\"Big Ideas Math Algebra 1 Answer Key Chapter 8 Graphing Quadratic Functions 8.6 35\" width=\"381\" height=\"310\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-35.png 381w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answer-Key-Chapter-8-Graphing-Quadratic-Functions-8.6-35-300x244.png 300w\" sizes=\"(max-width: 381px) 100vw, 381px\" \/><br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_Quadratic_Functions_Chapter_Review\"><\/a>Graphing Quadratic Functions Chapter Review<\/h3>\n<p><strong>8.1 Graphing f(x) = ax<sup>2<\/sup> (pp. 419\u2013424)<\/strong><\/p>\n<p><strong>Graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 1.<br \/>\np(x) = 7x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nq(x) = \\(\\frac{1}{2}\\)x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\ng(x) = &#8211; \\(\\frac{3}{4}\\)x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nh(x) = -6x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nIdentify characteristics of the quadratic function and its graph.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36077\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-cr-1.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions cr 1\" width=\"165\" height=\"151\" \/><br \/>\nAnswer:<\/p>\n<p><strong>8.2 Graphing f(x) = ax<sup>2<\/sup> + c (pp. 425\u2013430)<\/strong><\/p>\n<p><strong>Graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 6.<br \/>\ng(x) = x<sup>2<\/sup> + 5<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nh(x) = -x<sup>2<\/sup> &#8211; 4<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nm(x) = -2x<sup>2<\/sup> + 6<br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nn(x) = \\(\\frac{1}{3}\\)x<sup>2<\/sup> &#8211; 5<br \/>\nAnswer:<\/p>\n<p><strong>8.3 Graphing f(x) = ax<sup>2<\/sup> + bx + c (pp. 431\u2013438)<\/strong><\/p>\n<p><strong>Graph the function. Describe the domain and range.<\/strong><br \/>\nQuestion 10.<br \/>\ny = x<sup>2<\/sup> &#8211; 2x + 7<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\nf(x) = -3x<sup>2<\/sup> + 3x &#8211; 4<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\ny = \\(\\frac{1}{2}\\)x<sup>2<\/sup> &#8211; 6x + 10<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\nThe function f(t) = -16t<sup>2<\/sup> + 88t + 12 represents the height (in feet) of a pumpkin t seconds after it is launched from a catapult. When does the pumpkin reach its maximum height? What is the maximum height of the pumpkin?<br \/>\nAnswer:<\/p>\n<p><strong>8.4 Graphing f(x) = a(x \u2212 h)<sup>2<\/sup> + k\u00a0 \u00a0 (pp. 441\u2013448)<\/strong><\/p>\n<p><strong>Determine whether the function is even, odd, or neither.<\/strong><br \/>\nQuestion 14.<br \/>\nw(x) = 5<sup>x<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nr(x) = -8x<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nh(x) = 3x<sup>2<\/sup> &#8211; 2x<br \/>\nAnswer:<\/p>\n<p><strong>Graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 17.<br \/>\nh(x) = 2(x &#8211; 4)<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 18.<br \/>\ng(x) = \\(\\frac{1}{2}\\)(x &#8211; 1)<sup>2<\/sup> + 1<br \/>\nAnswer:<\/p>\n<p>Question 19.<br \/>\nq(x) = -(x + 4)<sup>2<\/sup> + 7<br \/>\nAnswer:<\/p>\n<p>Question 20.<br \/>\nConsider the function g(x) = -3(x + 2)<sup>2<\/sup> &#8211; 4. Graph h(x) = g(x = 1).<br \/>\nAnswer:<\/p>\n<p>Question 21.<br \/>\nWrite a quadratic function whose graph has a vertex of (3, 2) and passes through the point (4, 7).<br \/>\nAnswer:<\/p>\n<p><strong>8.5 Using Intercept Form (pp. 449\u2013458)<\/strong><\/p>\n<p><strong>Graph the quadratic function. Label the vertex, axis of symmetry, and x-intercepts. Describe the domain and range of the function.<\/strong><br \/>\nQuestion 22.<br \/>\ny = (x &#8211; 4)(x + 2)<br \/>\nAnswer:<\/p>\n<p>Question 23.<br \/>\nf(x) = -3(x + 3)(x + 1)<br \/>\nAnswer:<\/p>\n<p>Question 24.<br \/>\ny = x<sup>2<\/sup> &#8211; 8x + 15<br \/>\nAnswer:<\/p>\n<p>Use zeros to graph the function.<br \/>\nQuestion 25.<br \/>\ny = -2x<sup>2<\/sup> + 6x + 8<br \/>\nAnswer:<\/p>\n<p>Question 26.<br \/>\nf(x) = x<sup>2<\/sup> + x &#8211; 2<br \/>\nAnswer:<\/p>\n<p>Question 27.<br \/>\nf(x) = 2x<sup>2<\/sup> &#8211; 18x<br \/>\nAnswer:<\/p>\n<p>Question 28.<br \/>\nWrite a quadratic function in standard form whose graph passes through (4, 0) and (6, 0).<br \/>\nAnswer:<\/p>\n<p><strong>8.6 Comparing Linear, Exponential, and Quadratic Functions (pp. 459\u2212468)<\/strong><\/p>\n<p>Question 29.<br \/>\nTell whether the table of values represents a linear, an exponential, or a quadratic function. Then write the function.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36078\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-cr-2.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions cr 2\" width=\"261\" height=\"72\" \/><br \/>\nAnswer:<\/p>\n<p>Question 30.<br \/>\nThe balance y (in dollars) of your savings account after t years is represented by y = 200(1.1)t. The beginning balance of your friend\u2019s account is $250, and the balance increases by $20 each year. (a) Compare the account balances by calculating and interpreting the average rates of change from t = 2 to t = 7. (b) Predict which account will have a greater balance after 10 years. Explain.<br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_Quadratic_Functions_Chapter_Test\"><\/a>Graphing Quadratic Functions Chapter Test<\/h3>\n<p><strong>Graph the function. Compare the graph to the graph of f(x) = x<sup>2<\/sup>.<\/strong><br \/>\nQuestion 1.<br \/>\nh(x) = 2x<sup>2<\/sup> &#8211; 3<br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\ng(x) = &#8211;\\(\\frac{1}{2}\\)x<sup>2<\/sup><br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\np(x) = \\(\\frac{1}{2}\\)(x + 1)<sup>2<\/sup> &#8211; 1<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nConsider the graph of the function f.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36079\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-ct-4.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions ct 4\" width=\"205\" height=\"159\" \/><br \/>\na. Find the domain, range, and zeros of the function.<br \/>\nb. Write the function f in standard form.<br \/>\nc. Compare the graph of f to the graph of g(x) = x<sup>2<\/sup>.<br \/>\nd. Graph h(x) = f (x &#8211; 6).<br \/>\nAnswer:<\/p>\n<p><strong>Use zeros to graph the function. Describe the domain and range of the function.<\/strong><br \/>\nQuestion 5.<br \/>\nf(x) = 2x<sup>2<\/sup> &#8211; 8x + 8<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\ny = -(x + 5)(x &#8211; 1)<br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nh(x) = 16x<sup>2<\/sup> &#8211; 4<br \/>\nAnswer:<\/p>\n<p>Tell whether the table of values represents a linear, an exponential, or a quadratic function. Explain your reasoning. Then write the function.<br \/>\nQuestion 8.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36080\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-ct-8.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions ct 8\" width=\"223\" height=\"65\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36081\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-ct-9.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions ct 9\" width=\"225\" height=\"67\" \/><br \/>\nAnswer:<\/p>\n<p><strong>Write a quadratic function in standard form whose graph satisfies the given conditions. Explain the process you used.<\/strong><br \/>\nQuestion 10.<br \/>\npasses through (-8, 0), (-2, 0), and (-6, 4)<br \/>\nAnswer:<\/p>\n<p>Question 11.<br \/>\npasses through (0, 0), (10, 0), and (9, -27)<br \/>\nAnswer:<\/p>\n<p>Question 12.<br \/>\nis even and has a range of y \u2265 3<br \/>\nAnswer:<\/p>\n<p>Question 13.<br \/>\npasses through (4, 0) and (1, 9)<br \/>\nAnswer:<\/p>\n<p>Question 14.<br \/>\nThe table shows the distances d (in miles) that Earth moves in its orbit around the Sun after t seconds. Let the time t be the independent variable. Tell whether the data can be modeled by a linear, an exponential, or a quadratic function. Explain. Then write a function that models the data.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36082\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-ct-14.png\" alt=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions ct 14\" width=\"304\" height=\"66\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-ct-14.png 304w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Answers-Chapter-8-Graphing-Quadratic-Functions-ct-14-300x65.png 300w\" sizes=\"(max-width: 304px) 100vw, 304px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 15.<br \/>\nYou are playing tennis with a friend. The path of the tennis ball after you return a serve can be modeled by the function y = -0.005x<sup>2<\/sup> + 0.17x + 3, where x is the horizontal distance (in feet) from where you hit the ball and y is the height (in feet) of the ball.<br \/>\na. What is the maximum height of the tennis ball?<br \/>\nb. You are standing 30 feet from the net, which is 3 feet high. Will the ball clear the net? Explain your reasoning.<br \/>\nAnswer:<\/p>\n<p>Question 16.<br \/>\nFind values of a, b, and c so that the function f(x) = ax<sup>2<\/sup> + bx + c is (a) even, (b) odd, and (c) neither even nor odd.<br \/>\nAnswer:<\/p>\n<p>Question 17.<br \/>\nConsider the function f(x) = x<sup>2<\/sup> + 4. Find the average rate of change from x = 0 to x = 1, from x = 1 to x = 2, and from x = 2 to x = 3. What do you notice about the average rates of change when the function is increasing?<br \/>\nAnswer:<\/p>\n<h3><a id=\"Graphing_Quadratic_Functions_Cumulative_Assessment\"><\/a>Graphing Quadratic Functions Cumulative Assessment<\/h3>\n<p>Question 1.<br \/>\nWhich function is represented by the graph?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36083\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-1.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions ca 1\" width=\"369\" height=\"163\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-1.png 369w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-1-300x133.png 300w\" sizes=\"(max-width: 369px) 100vw, 369px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 2.<br \/>\nFind all numbers between 0 and 100 that are in the range of the function defined below.(HSF-IF.A.3)<br \/>\nf(1) = 1, f(2) = 1, f(n) = f(n &#8211; 1) + f(n &#8211; 2)<br \/>\nAnswer:<\/p>\n<p>Question 3.<br \/>\nThe function f(t) = -16t<sup>2<\/sup> + v<sub>0<\/sub>t + s<sub>0<\/sub> represents the height (in feet) of a ball t seconds after it is thrown from an initial height s0 (in feet) with an initial vertical velocity v0 (in feet per second). The ball reaches its maximum height after \\(\\frac{7}{8}\\) second when it is thrown with an initial vertical velocity of ______ feet per second.<br \/>\nAnswer:<\/p>\n<p>Question 4.<br \/>\nClassify each system of equations by the number of solutions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36084\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-4.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions ca 4\" width=\"410\" height=\"162\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-4.png 410w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-4-300x119.png 300w\" sizes=\"(max-width: 410px) 100vw, 410px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 5.<br \/>\nYour friend claims that quadratic functions can have two, one, or no real zeros. Do you support your friend\u2019s claim? Use graphs to justify your answer.<br \/>\nAnswer:<\/p>\n<p>Question 6.<br \/>\nWhich polynomial represents the area (in square feet) of the shaded region of the figure?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36085\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-6.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions ca 6\" width=\"442\" height=\"175\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-6.png 442w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-6-300x119.png 300w\" sizes=\"(max-width: 442px) 100vw, 442px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 7.<br \/>\nConsider the functions represented by the tables.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36086\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-7.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions ca 7\" width=\"492\" height=\"141\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-7.png 492w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-7-300x86.png 300w\" sizes=\"(max-width: 492px) 100vw, 492px\" \/><br \/>\na. Classify each function as linear, exponential, or quadratic.<br \/>\nb. Order the functions from least to greatest according to the average rates of change between x = 1 and x = 3.<br \/>\nAnswer:<\/p>\n<p>Question 8.<br \/>\nComplete each function using the symbols + or &#8211; , so that the graph of the quadratic function satisfies the given conditions.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36087\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-8.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions ca 8\" width=\"377\" height=\"148\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-8.png 377w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-8-300x118.png 300w\" sizes=\"(max-width: 377px) 100vw, 377px\" \/><br \/>\nAnswer:<\/p>\n<p>Question 9.<br \/>\nThe graph shows the amounts y (in dollars) that a referee earns for refereeing x high school volleyball games.<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36088\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-9.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions ca 9\" width=\"213\" height=\"258\" \/><br \/>\na. Does the graph represent a linear or nonlinear function? Explain.<br \/>\nb. Describe the domain of the function. Is the domain discrete or continuous?<br \/>\nc. Write a function that models the data.<br \/>\nd. Can the referee earn exactly $500? Explain.<br \/>\nAnswer:<\/p>\n<p>Question 10.<br \/>\nWhich expressions are equivalent to (b<sup>-5<\/sup>)<sup>-4<\/sup>?<br \/>\n<img loading=\"lazy\" class=\"alignnone size-full wp-image-36089\" src=\"https:\/\/ccssmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-10.png\" alt=\"Big Ideas Math Algebra 1 Solutions Chapter 8 Graphing Quadratic Functions ca 10\" width=\"452\" height=\"99\" srcset=\"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-10.png 452w, https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/01\/Big-Ideas-Math-Algebra-1-Solutions-Chapter-8-Graphing-Quadratic-Functions-ca-10-300x66.png 300w\" sizes=\"(max-width: 452px) 100vw, 452px\" \/><br \/>\nAnswer:<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions Pdf of all exercises along with extra practice sections, quizzes, chapter tests, cumulative assessment, etc. are provided here. Students who are searching for the perfect study guide to enhance their math skills can refer to this Big ideas math algebra 1 ch 8 answer &#8230; <a title=\"Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/big-ideas-math-algebra-1-answers-chapter-8\/\" aria-label=\"More on Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":89142,"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-8-Graphing-Quadratic-Functions.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35943"}],"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=35943"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35943\/revisions"}],"predecessor-version":[{"id":90379,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/35943\/revisions\/90379"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/89142"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=35943"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=35943"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=35943"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}