Step 3: Question 2. f(x) = \(\frac{1}{2}\)x2 3x 4 Explain your reasoning. Answer: f(x) = -2x 2. Now we have to substitute x = -2 in the above expression f(12) = f(11) + f(10) = 89 + 55 = 144 In what year were the populations about equal? Find the x-coordinate where y = 0 which is at x = 90 = f(b) f(a)/b-a Satellite dishes are shaped like parabolas to optimally receive signals. The x-intercepts of the given function are 0 and 2. average rates of change from t = 2 to t = 7 x = 1 or x = -2 Find another point on the parabola. Question 39. In Exercises 3944, graph the function. Step 1: Graph the axis of symmetry: h = 59, axis of symmetry is x = 59. How can you describe the graph of f(x) = a(x h)2? \(\frac{7}{3}\). p(x) = \(\frac{1}{3}\)x2 2 b. g(-x) = 3x2 The zeros also the x-intercepts: 3, 7 Step 2: Point 1: (0, -2) Question 35. Question 73. a. Graph each function. Answer: f(x) = 5(x 1)(x 3)(x 6) How far from each tower shown is the lowest point of the cable? The cable is about 203 feet above the water at its lower point. Answer: Tell whether the points appear to represent a linear, an exponential, or a quadratic function. The first differences are: -12, -12, -12 Here, we have given a complete guide of Chapter 8 BIM Algebra 1 Graphing Quadratic Functions Answers in quick links. Hence the vertex is (-3, -4), Question 3. y c if if a < 0 The ball reaches its maximum height after \(\frac{7}{8}\) second when it is thrown with an initial vertical velocity of ______ feet per second. The y-intercept is (0, 36) h(x) = 2(x 4)2 Thus maximum height is 18 feet and after achieving it the softball hits the ground. Therefore the function that represents the given table of values is f(x) = 8 . x2 36 = 0 We observe that the two graphs have the same vertex, range, axis of symmetry and are both parabolas. Answer: Thus, g is an even function. Substituting x = 0, the y-intercept is f(x) = -2x + 16x, Question 56. y = -3x2 + 6x + 9 (x + 8)(x 8) f(9) = f(8) + f(7) = 21 + 13 = 34 Big Ideas Learning, LLC. We note that both graphs are parabolas and have the same range and axis of symmetry. bx Using Your Book . Therefore the data must represent an exponential function with a base of 0.5 or 1/2. Range: 0 f(x) 25, b. y c if a > 0 or Boswell, Laurie; Big Ideas Learning, LLC Boxid IA40320904 Camera USB PTP Class Camera Collection_set printdisabled External-identifier urn:oclc:record:1301804939 urn:lcp:bigideasmathalge0000lars_c4s3:lcpdf:43feba2e-89dc-4012-8ca3-5561757632b0 x = 7/2. Given, If x = 1 \(\frac{1}{2}\)(1) 2 = -2\(\frac{1}{2}\) f(x) = \(\frac{1}{2}\)(2)2 + 2(2) + 16 = 18 Answer: f(x) = -1/12(x 59)2 + 300 Substitute the intercepts and simplify: r(x) = -8x 1 0 = (x 1)(x + 2) Let k be a constant. The second differences are: -8, -8 Compare the graph to the graph of f(x) = x2. The balance y (in dollars) of your savings account after t years is represented by y = 200(1.1)t. The beginning balance of your friends account is $250, and the balance increases by $20 each year. Question 31. 3( x2 4x + 4) = 0 ERROR ANALYSIS c. Which polynomial represents the area (in square feet) of the shaded region of the figure? x = \(\frac{-b}{2a}\) Question 29. Direct link to 054775's post Great product.but it w, Posted 5 years ago. Therefore, there are infinitely many solutions. g(x) = 6x2 Therefore there is 1 solution. 3x2 = 27 Question 23. Thus the range is (-, 18]. f(x) = 3x2 2x The function g(x) = f(x) 9 involves subtraction of 9 to f(x) therefore g(x) involves a 9 unit shift downward of the graph of f(x), Question 11. y = a(x-p)(x-q) vertical stretch by a factor of 3 f(x) = \(\frac{1}{3}\)(x + 5)(x 1) Question 3. The function completely and the zeros are: 0, -9, -3. It is not possible to write a quadratic function represented by the table. point 2: (-1, 6) Answer: Let the diameter d represent the independent variable. Question 15. Answer: (-3, 5), (0, -1), (2, -5), (-4, 7), (1, -3) Answer: vertex: (-2, -4); passes through (-1, -6) x = -5 or x = 6, Question 42. Thus each pattern represents exponential function with common factor 2. If x = 0 -3(0) + 4 = 4 Question 43. Answer: Question 8. f(x) = x 6x. Answer: f(x) = (x + 4)(x + 1) f(x) = 5x2 + 10x 3 Answer: Question 99. a. Displaying all worksheets related to - Student Jouranal Big Ideas Math Grade 7 51 Practice. The function g(x) = f(x) 6 involves subtraction of 6 to f(x) therefore g(x) involves a 6 unit shift downward of the graph of f(x) The graph of an even function is symmetric about the y-axis. = 20 9 Answer: Given, p = 6 and q = 10 c. The range implies that the parabola opens upward and the y-coordinate is -6 1 = -12 + 1 y = 2x2 10x + 13 = -16 4 6 Answer: Note that the graph has an equation of y = -x + 4 because of reflection in the x-axis and vertical translation. Answer: Answer: The Big Ideas Math: Modeling Real Life program comes with built-in parent support. a = 5 Let f(x) be an odd function. The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. 3x 9 = 0 or 4x + 12 = 0 Using the vertex form, the graph of f(x) is the graph of g(x) is: Graph the axis of symmetry x = 0 + 8/2 = 4 = -25. At vertex (h, k) = (0, 3) The graph is shifted to the left by 6. Answer: Question 1. y = \(\frac{1}{2}\)x 2 Question 2. Does Practicing from Algebra 1 Big Ideas Math Solutions help you score better grades? g(x) = -4x2 8x 4 Written by renowned authors, Dr. Ron Larson and Dr. Laurie Boswell, Algebra 1, Geometry, and Algebra 2 are a true extension of the Big Ideas Math: Modeling Real Life K-8 series, creating one cohesive voice from kindergarten through Algebra 2. y = -4 Answer: If x = 1 -3(1) + 4 = 1 ax12 + b1 + c = y1 c Answer: Question 94. In Exercises 1320, graph the quadratic function. The graph of g is a horizontal translation h units right if h is positive or |h| units left if h is negative and a vertical translation k units up if k is positive or |k| units down if k is negative of the graph of f. Question 4. y = x2 + 6x + 5 f(x) = a(x h)2 + k y = x2 + 4x 5 At a basketball game, an air cannon launches T-shirts into the crowd. y(0) = (0 2)(0 + 2) = -4 y = (0)3 4(0)2 11(0) + 30 = 30 The U-shaped graph of a quadratic function is called a parabola. This corresponds to Graph A. Describe and correct the error in finding the axis of symmetry of the graph of y = 3x2 12x + 11. Which function has a growth rate that is eventually much greater than the growth rates of the other two functions? 2x + 6 = 0 Answer: p = -3 and q = 4 Answer: Question 78. y = \(\frac{7}{4}\)x + 3 b. 14 day loan required to access PDF files. Which birdbath is wider? MODELING WITH MATHEMATICS The softball attains the maximum height at the vertex. Axis of symmetry: x = -1 ERROR ANALYSIS The points from a straight line. b. A = (x a) Answer: 9a 1 = 2 f(x) = -2(x 4)2 8 ft. Thus the function You can click directly from the PDF to go to resources on the Khan Academy website. f(x) = a(x +8)(x + 3)(x) Answer: Question 36. First difference: 49.7, 63.9, 78.1 Question 107. https://play.google.com/store/apps/details?id. Free Easy Access Student Edition - Common Core High School. x-intercept: (-3, 0) and (3, 0) Answer: Explain. The function is odd if it satisfies: = 4 Write an equation that represents g in terms of x. Now we have to substitute x = -2 in the above expression The function y = ax2 is derived from the parent function y = x2 by various transformation: vertical stretch (|a| > 1) or contraction (0 < |a| < 1) and reflection about the x-axis. Answer: Vertex: (3, 6) (120 6n) represents the unit price so we need to find the value of n where R is maximum which is located at the vertex. Given, Question 2. System C: Use a graph to justify your answer. Range: [5, -), Graph the function. g(x) = f(x) + h(x) b. Answer: Question 10. (x 4)(x 13) = 0 The 2 equations are the same line. y = 3.6 ft How to Solve Big Ideas Math Algebra 1 Textbook Questions easily? Answer: y = 2x2 8x + 8 y = 36 The height is approximately 60 feet Answer: g(x) = x2 + 6 MODELING WITH MATHEMATICS h(x) = \(\frac{1}{4}\)x2 The function y = a(x-h) + k has vertex as (h, k) and derived from the parent function y = x by various transformations: vertical shift of |k| units, horizontal of |h| units, vertical stretch or contraction (0 < |a| < 1) and reflection about the x-axis. A = -2x + 8x + 24 y intercept is c = 13. Answer: Answer: Does changing the value of p change the x-intercepts? Work with a partner. Graph f(x) = g(x) 3 y = 4x2 Question 13. Question 1. = 14, Question 34. Question 21. Answer: Answer: Therefore, the 2 factors will have opposite signs: Explain how you found the x-intercepts. Answer: He conducted meta-analyses and compared the . x-intercepts: -7, -5, and 0 Explain your reasoning. = 100/5 = 200 Compare the graph to the graph of f(x) = x2. The cable is at road level midway between the towers. Answer: y = a(x h) + k What is the U-shaped graph of a quadratic function called? Compare the graph to the graph of f(x) = x2. Question 1. In Exercises 712, graph the quadratic function. Ace up your preparation and Develop Problem Solving Skills by referring to the Ch 8 Graphing Quadratic Functions Big Ideas Math Book Algebra 1 Solution Key. x = 1, 3, -3. Compare the speeds of the three cars. The graph is a translation left 2 units and a vertical stretch by a factor of 2 of the graph y = x2. The error is that the graph g(x) = x2 10 is the graph of f(x) = x2 translated down by 10 units instead of up. passes through (1, 0) and (7, 0) Answer: Question 2. Answer: Answer: Question 49. 7/8 = v0/32 f(x) = 3(x + 1)(x 1)(x 2) For s(x): Answer: Big Ideas Math Book Algebra 1 Solution Key, Graphing Quadratic Functions Maintaining Mathematical Proficiency Page 417, Graphing Quadratic Functions Mathematical Practices Page 418, Lesson 8.1 Graphing f(x) = ax2 Page (419-424), Graphing f(x) = ax2 8.1 Exercises Page (423-424), Lesson 8.2 Graphing f(x) = ax2 + c Page (425-430), Graphing f(x) = ax2 + c 8.2 Exercises Page (429-430), Lesson 8.3 Graphing f(x) = ax2 + bx + c Page (431-438), Graphing f(x) = ax2 + bx + c 8.3 Exercises Page (436-438), Graphing Quadratic Functions Study Skills: Learning Visually Page 439, Graphing Quadratic Functions 8.1 8.3 Quiz Page 440, Lesson 8.4 Graphing f(x) = a(x h)2 + k Page (441-448), Graphing f(x) = a(x h)2 + k 8.4 Exercises Page (446-448), Lesson 8.5 Using Intercept Form Page (449-458), Using Intercept Form 8.5 Exercises Page (455-458), Lesson 8.6 Comparing Linear, Exponential, and Quadratic Functions Page (459-468), Comparing Linear, Exponential, and Quadratic Functions 8.6 Exercises Page (465-468), Graphing Quadratic Functions Performance Task: Asteroid Aim Page 469, Graphing Quadratic Functions Chapter Review Page (470-472), Graphing Quadratic Functions Chapter Test Page 473, Graphing Quadratic Functions Cumulative Assessment Page (474-475), Big Ideas Math Answers Grade 7 Accelerated, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 4 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 3 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 2 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 7 Module 1 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 7 Module 2 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 7 Module 3 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 3 Module 2 Answer Key, Bridges in Mathematics Grade 4 Student Book Unit 3 Module 1 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 8 Module 4 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 8 Module 3 Answer Key, Bridges in Mathematics Grade 2 Home Connections Unit 8 Module 2 Answer Key. Is your friend correct? g(x) = (x 1)(x 3)(x + 3) b. In Exercises 2126, tell whether the function has a minimum value or a maximum value. = 4 16 + 5 3x2 + x 2 x2 = 9 c = h + k Solving a and b, a = 1.5, b = -0.5 The breaking strength z (in pounds) of a manila rope can be modeled by z = 8900d2, where d is the diameter (in inches) of the rope. Vertically stretched by a factor of 2 4, 5, 9, 14, 23, . Question 39. Essential Question How can you describe the graph of f(x) = a(x h)2? Match the function with its graph. R(n) = (120 4n)(80 + 5n) x + 4 = 0 or x + 3 = 0 or x 3 = 0 5 = a(6 1)(6 7) Question 26. Question 103. Answer: The main difference between the two graphs is that the graph of the given function is the graph of f(x) = x2 translated up by 6 units. Thus the function is odd, Question 2. Compare the absolute values of the rate of change, the order from least to greatest is: t(x), p(x), r(x), s(x), Question 8. -3a = 3 a. 5(-2)2 9 Question 3. a = -2 a. Answer: Describe the transformation(s) from the graph of f(x) = |x| to the graph of the given function. Consider 0 < a < 1, a> 1, -1 < a < 0, and a < -1. x = \(\frac{b}{2a}\) Explain. CRITICAL THINKING f(x) = a(x 1)2 + 2 b(x) = 2.5x2 g(x) = f(x) 6 w(x) = 5x Question 6. 4 unit shift downward, Question 21. a < -1. Given function Answer: Answer: f(x) = ax2 + bx + c Plot the corresponding points: (0, 0), (5, 0) 4r 36s. Match each graph with its function. a = \(\frac{3}{4}\) and b = 9 In Exercises 58, tell whether the points appear to represent a linear, an exponential, or a quadratic function. h(x) = -4(x 7)(x 3) Answer: Axis of symmetry: x = 6. y = -x2 + 4x + 12 Question 37. f(x) = -3x2 + 12; g(x) = f(x) 9 HOW DO YOU SEE IT? g(x) = -4x2 8x 4 Question 13. s(x) = 18-(72)/3-1 = -27 x 4 = 0 or x + 1 = 0 Question 17. Therefore the equation of the quadratic function is y = -2 x2, Write a quadratic function in standard form whose graph satisfies the given conditions. USING TOOLS a 4 unit shift to the left If a common ratio exists consecutive y-values, an exponential function must be used to model a data set. Therefore there is 1 solution. g(x) = 2x Getting helpful and educational math answers and solutions to high school Algebra 1 exercises could be the key to . Answer: Use Mathleaks to get learning-focused solutions and answers to Algebra 1 math, either 8th grade Algebra 1 or 9th grade Algebra 1, for the most commonly used textbooks from publishers such as Houghton Mifflin Harcourt, Big Ideas Learning, CPM, McGraw Hill, and Pearson. Explain how you can tell whether a quadratic function has a maximum value or a minimum value without graphing the function. y(-3) = 4(-3)2 + 24(-3) + 13 15 = 4a + k Then, learn thoroughly & solve all BIM Algebra 1 Ch 8 Graphing Quadratic Functions Questions covered in the chapter test, quiz pages. Plot the ordered pairs and draw a smooth curve through the points. Consider the functions represented by the tables. Students meet a National Geographic Explorer at the beginning of each chapter to learn how they apply mathematics in their profession with an Everyday Explorations video. 8(x + 1)(x 1) = 0 g(-x) = 2(-x) = -2x The function y = ax2 is derived from the parent function y = x2 by various transformation: vertical stretch (|a| > 1) or contraction (0 < |a| < 1) and reflection about the x-axis. Answer: x = -6 or 6 or 11, Question 30. b = -2ahx Question 39. x 6 = 0 or x 1 = 0 b. If so, by how much? Given, Find the axis of symmetry and vertex: Answer: Width of arch = 500 (-500) (x 5) (x 3) = 0 Question 7. The End-of-Course Assessment is modeled after the ADP Algebra 1 test and can serve as practice before taking the actual ADP test. So we replace x with w(x) with -x Answer: Question 6. Given, -2 = a(1) Answer: Question 46. Answer: Essential Question How can you find the vertex of the graph of f(x) = ax2 + bx + c? g(x) = x2 + x 12 Deductive Reasoning In Exercises 1316, describe the transformation from the graph of f to the graph of g. Then graph f and g in the same coordinate plane. y = -4 f(x) = a(x p)(x q)(x r) Step 1: The x-intercepts are 3 and -4. How are the graphs in Monitoring Progress Questions 1-8 similar? Given, (x2, y2) (4, 180) (-2, 8), (-1, 0), (0, -4), (1, -4), (2, 0), (3, 8) Question 95. y = \(\frac{1}{2}\)x2 + 7x 4 Let the time t be the independent variable. Explain. The vertex is (-1, 1). f(x) = -6(x + 3)(x)(x 2) Answer: PROBLEM SOLVING In Exercises 100 and 101, write a system of two quadratic equations whose graphs intersect at the given points. g(x) = 2(x 1)2 2 Question 67. Answer: f(-1) = -2(-1)2 4(-1) + 30 = 32 f(x) = x 16x + 72. Describe and correct the error in graphing the function f(x) = -x2+ 4x + 3. Question 4. Compare the websites in Example 4 by calculating and interpreting the average rates of change from Day 0 to Day 10. First we will graph the function and find the axis of symmetry In Exercises 512, determine whether the function is even, odd, or neither. x = -b/2a All the Big Ideas Math Solutions are given by subject experts adhering to the Common Core 2019 Curriculum. Answer: a = 3 The height (in meters) of a bird diving to catch a fish is represented by h(t) = 5(t 2.5)2, where t is the number of seconds after beginning the dive. The graph of h(x) is a vertical shrink by a factor of 1/3 of the graph of f(x) g(x) = f(x 1) Question 4. A student takes a subway to a public library. f(x) = 3(x 3)2 + 6 Let f, h be even function. g(x) = 2(x)(x 2) The values p and q are x-intercepts of the graph of the function f(x) = a(x p)(x q). Big Ideas Learning Algebra 1_Geometry_Algebra 2 Program Overview - Cengage . Since t1 > 0, we have x = 0 a. COMPARING FUNCTIONS At (0, 0): 0 = a(0) + b(0) + c Answer: Graph r. a = 1 Since the second differences are constant, then it is quadratic. The quadrants of the graphs are different and they are not equal to zero. Question 5. Thus the points (2, 0) and (-2, 0) lie on the graph. m(x) = -2x2 + 6 In Exercises 7174, describe the transformation from the graph of f to the graph of h. Write an equation that represents h in terms of x. Looking for the Topic-wise Big Ideas Math Algebra 1 Answers Chapter 8 Graphing Quadratic Functions for growing your Math Skills? -x2 + 4x + 1 y = x + 2x 8 g(x) = f(x) + 7 -4 = m 2 Question 6. x = -3 -2 = -4a So we replace x with r(x) with -x Answer: Question 78. -4x2 + 2x 6 Graph the axis of symmetry x = -9 + 3/2 = -3 g(x) = f(x) + ah(x) = g(x) f(-x) = -5x Request your sample of Algebra 1, Geometry, and Algebra 2 from National Geographic Learning. y = x2 17x + 52 The table shows the distances d (in miles) the student travels in t minutes. If x = 1 2(1) 3 = -1 Question 14. f(x) = 6.38(1.11)x Use graphs to justify your answer. f(x) = 2x2 4x For what length of vacation does each resort cost about the same? Throughout each chapter, students develop their mathematical skills by following the Explorers research and creating STEM connections. (x 6)(x 1) = 0 Therefore, the first pinecone will hit the ground in the least amount of time. The function is even is it satisfies: Describe the domain and range of the function. Answer: Graph the function. Therefore, there are infinitely many solutions. Compare the graph to the graph of f(x) = x2. Can a quadratic function with exactly one real zero be written in intercept form? Question 40. The y-values have a common 2nd difference therefore the table of values represents a quadratic function. = -4 8 + 1 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). In the function f(x) = a(x p)(x q) Question 71. y = 3x2 + 2x on December 27, 2021, There are no reviews yet. a = 4 and b = -3 -4x2 + 2x 6 4y(4y 2) + 2(4y 2) Question 3. 3x = 9 or 4x = -12 f(x) = -19/9(x + 3)2 + 5. To find the value of a, substitute the x and y values of the point on the parabola (6, 5) Request Samples and Digital Access. The axis of symmetry is -1/3 = -6(2)2 + 24(2) 20 y = x2 17x + 52 Answer: f(x) = -1(x +8)(x + 3)(x) x2 = 36 a> 1 Answer: Question 26. Answer: Answer: Question 106. Question 16. \(\frac{1}{3}\)(x + 5)(x 1) = 0 Work with a partner. -4 = -a(6) Answer: Question 1. MATHEMATICAL CONNECTIONS Work with a partner. Answer: f(x) = -(x + 5))2 6 Which is different? Big Ideas Math - Algebra 1, A Common Core Curriculum Larson, Ron; Boswell, Laurie Publisher Big Ideas Learning LLC ISBN 978-1-60840-838-2. x + 5 = 0 or x 6 = 0 b. Answer: A portion of a roller coaster track is in the shape of a parabola. 9/9/15 2:20 PM. \(\frac{1}{2}\)(-(x + 1)2 + 2) = \(\frac{1}{2}\)(x + 1)2 + 1. The quadratic is even if it is symmetric about the y-axis so the symmetry is the y-axis. Question 23. y = a . Question 53. Describe and correct the error in writing the function represented by the table. The Big Ideas Math: Modeling Real Life series comes with two options of accelerating students, the Advanced Pathway and the Compacted Pathway. y = 4x2 + 24x + 13 b. So, the exponential function is Complete each function using the symbols + or , so that the graph of the quadratic function satisfies the given conditions. f(x) = a . a = -2, b = 8 Question 19. notice that w(-x) is not equal to -w(x) = -5x or w(x) REASONING State the vertex and axis of symmetry of the graph of y = ax2 + c. As the graph passes through the point (4, 7). Answer: y = a(x + 2x 8) The ball will clear the net if at x = 30, the height, y, is greater than 3 feet. The domain is the set of real numbers. The parabola opens downward with the following characteristics Your friend claims that any quadratic function can be written in standard form and in vertex form. Answer: y = -1/3 g(x) = 5(x + 1)(x + 2) Answer: Question 20. Identify characteristics of the quadratic function and its graph. Solve linear equations with variables on both sides. Question 11. Answer: y = 0 To find the value of a, substitute the x and y values of the point on the parabola (6, 5) y = -3x + 4 a. x = 9/2(-\(\frac{3}{4}\)) Answer: System F: f(x) = 5(x 3)2 1; g(x) = (x) 6 The graph of f(x) = x2 is wider than the graph of g(x) = x2 when 0 < |a| < 1. f(x) = a[x (-2)][x (-5)] where, x N [1, n] f(2) = 1 Question 13. p = 120 6(5) There is no real zero when the graph does not cross/touch the x-axis. Question 4. The paths of water from three different garden waterfalls are given below. Answer: Question 68. p(x) = -5x2 10x 2 Then determine the type of function that best represents this situation. Answer: Explain why only nonnegative values of t are used in Example 4. y = x + 5 This is because the three other graphs are parabolas which are graphs of quadratic functions. Explain your procedure. h(x) = -x2 y = \(\frac{1}{3}\)(x + 5)2 2. The graph is symmetric about the origin. Answer: Question 2. x = -b/2a -1 = a 4 f(x) = a(x h)2 + k Explain your reasoning. c. 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. given, Answer: Question 32. y = x2 x 30 Answer: Answer: x = -1 f(11) = f(10) + f(9) = 55 + 34 = 89 Determine whether the sequence is arithmetic, geometric, or neither. y = (x + 5)(x + 3) y = 36 represents 36 ft, the initial height the apple was dropped. For r(x): Write a quadratic function whose graph has a vertex of (1, 2). y = x3 4x2 11x + 30 The function y = a(x-h) + k has vertex as (h, k) and derived from the parent function y = x by various transformations: vertical shift of |k| units, horizontal of |h| units, vertical stretch or contraction (0 < |a| < 1) and reflection about the x-axis. Range: {y R : y 25/2}, Question 3. The Algebra 1, Geometry, and Algebra 2 program purposefully integrates five key strategies proven to have the highest impact on student achievement. -2 vertex: (5, -2); passes through (7, 0) The population of Town A in 1970 was 3000. Answer: Question 48. ERROR ANALYSIS PROBLEM SOLVING y = (x 5)(x 3) m = (d2-d1)/(t2-t1) = (38-19)/2-1 = 19 Answer: In Exercises 8184, sketch a parabola that satisfies the given conditions. Answer: Answer: Question 30. x = 3/2 = 1.5 f(x) = a(x 2)2 + 4 does not belong because it is the only graph that will not have a vertical stretch or shrink. x from -2.3 to 0.3, Question 5. Step 3: Find and plot the vertex. Answer: Question 86. Your friend says all absolute value functions are even because of their symmetry. Question 27. In Exercises 5762, write a quadratic function in vertex form whose graph has the given vertex and passes through the given point. 8 = a . Finding y-coordinate for x = 29, we get that (29, 225) lies on the graph. (4y + 2)(4y 2) y = 02 0 30 = -30 Use the vertex form: 3x2 12x + 12 = 0 Answer: y = a(x h) + k h(x) = 8x2 8 Question 25. The system is consistent. g(x) = \(\frac{1}{4}\)x2 What definition and characteristics of the graph of a quadratic function did you use to answer Exercise 44 on page 438? (-2r + 6s)(-2r 6s) Consider the graph of the function f. Question 15. The axis of symmetry is at x = -b/2a The domain is the set of real numbers. Even, Question 8. CRITICAL THINKING Graph of 2.5x2 is narrower than x2 since it is stretched vertically by factor 2.5. Answer: y = -x2 + 4x + 12 Axis of symmetry is x = -2 f(x) = \(\frac{1}{15}\) (x 3)(x 13) Answer: Question 76. a. As the function is increasing, the rate of change also increases. Answer: Question 7. Then find the value. g(1) = 2 -g(-1) = 0 Question 7. Explain your reasoning. "Algebra 1, Geometry, and Algebra 2 make up an outstanding series together, making the math content come alive, via a plethora of colorful pictures sprinkled in on each page, as well as short snapshots of individual National Geographic Explorers, whose research connects the math content introduced in each chapter. y = -x + 7 x(x 1) = 0 -40 = a(5 1)(5 3)(5 6) The pinecone hits the ground at y = 0 When does the graph of a quadratic function open up? The player will make the shot if the point (3, 0) is on the parabola. MODELING WITH MATHEMATICS The vertex is at (h, k) and -8x2 + 98 = 0 Differentiate Minimum value: -8, Question 18. Explain your reasoning. The second differences are: 10, 10 = -24 + 48 20 Answer: Step 3: Use the y-intercept to find two more points on the graph. g(x) = 6x(x 1)(x + 6) y = -3x2 + 6x + 9 m(x) = 2x2 7x a = 4 and b = -3 Question 25. f(x) = \(\frac{1}{2}\)x x = -b/2a When a quadratic function is in standard form, completing the square can be applied so that it can be transformed to vertex form. Suppose the initial height is adjusted by k feet. (x + 3)(x 3) = 0 Write an equation that represents g in terms of x. Answer: If x = 3 \(\frac{1}{2}\)(3) 2 = \(\frac{7}{2}\) Answer: The third graph from the left does not belong to the group. substitute: h(x) = 2x2 + 3 f(x) = -4x2 + 4x 2 Answer: f(x) = (x 6)(x 1) Question 10. From t = 1 to t = 2: y = -0.4x2 Step 1: The x-intercepts are 3 and -5. 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. f(x) = 3x2 + 4 since h = -2 and k = -3. Question 77. Question 13. Answer: Given, f(x) = \(\frac{1}{9}\)(x 30)2 + 25 Step 1: The x-intercepts are 7 and 3. Answer: Then we know that -1 < a < 0. y = -(3)(-3) Answer: Question 52. In the given function n(x) = \(\frac{1}{3}\)x2 5 When your ball hits the ground, what is the height of your friends ball? f(x) = -2x + 10. Question 31. g(x) = f(x) + 2 y = (x 2)(x + 2) When a < 0 it opens down x = 1.5 represents 1.5s, the time the apple will hit the ground. Answer: The graph is neither even nor odd because it is not symmetric about the y-axis or the origin. g(x) = 2(x + 3)2 So, the vertex is (4, -16) Question 37. The error was in solving the equation x2 9 = 0 in a wrong way. 5 . By using the grid lines as guide, we can find an exact point by going 1 unit up and 1 unit to the right which means the slope is m = rise/run = 1 Let g(x) = f(x) + ah(x) Answer: Question 18. The data has no constant first nor second difference. Plot the points (0, 0) and (8, 0) Question 6. Question 3. Does the graph open up or down? Thus is equivalent to the function f(x) = 2 . y = a(x + 2)2 + k The function completely and the zeros are: 0, 1, -6 Answer: Question 34. Answer: x-intercept:(-1, 0) and (4, 0) Given function Question 8. Question 10. Answer: x 4 = 0 or x + 2 = 0 Explain your reasoning. Use the vertex form: x = 4 or x = 13, Question 26. Use the recursive rule until the term is greater than 100 where it is not included: Answer: Explain your reasoning. If x = 4 -3(4) + 4 = -8, Question 3. h(x) = (x2 36)(x 11) Answer: Question 24. = 3x2 + 2. Consider the function g(x) = -3(x + 2)2 4. x = -4/2(-1) Answer: y = 32. g(x) = x2 5 Or is this just a teaser? f(8) = f(7) + f(6) = 13 + 8 = 21 Suppose Blue Water Resort charges $1450 for the first three nights and $105 for each additional night. f(-1/2) = -4(-1/2)2 4(-1/2) + 7 = 8 Answer: Question 62. Question 17. Answer: Answer: x = -8/4 Answer: Question 2. 0, 1, 5, 12, 22 The vertex of a parabola is (3, -1). Answer: Question 3. 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