Answer: Which waterfall drops water from the highest point? Which function could include the point (-2, 3)? (-4, -4), (-2, -3.4), (0, -), (2, -2.6), (4, -2) f(x) = x 16x + 72. f(x) = 1(x + 2)(x 1) y = (x-h) + k a=1 Just click on the chapter you wish to prepare and start your preparation. Explain. 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. Answer: A professional basketball players shot is modeled by the function shown, where x and y are measured in feet. Plot the points. f(-0.5) = -2(-0.5 3)(-0.5 + 4) = 24.5 Answer: Question 96. y = (x + 5)(x + 3) Answer: Graph the quadratic function. MAKING AN ARGUMENT point 2: (4, -2). 8(x + 1)(x 1) = 0 Answer: The slopes are different so they intersect. Here comes the best & helpful guide ie., Big Ideas Math Algebra 1 Answers Chapter 7 Polynomial Equations and Factoring. Core Concepts y = 2x2 10x + 13 m = (d2-d1)/(t2-t1) = (38-19)/2-1 = 19 So we replace x with r(x) with -x Answer: Answer: (-1, -3), (-3, 5), (0, -1), (1, 5), (2, 15) Given, At a basketball game, an air cannon launches T-shirts into the crowd. Finding y-coordinate for x = 29, we get that (29, 225) lies on the graph. (x + 3)(x 3) = 0 a. Answer: Graph the function. p(x) = 3(x 1)2 x-intercepts: -7, -5, and 0 From the graph, we can see that the quadratic function opens upward and the vertex is (1, -3) Point 1: (3, 3) f(x) = mx 2 You can use the BIM Math Textbook Answers Algebra 1 for reference and we dont charge any amount for the help. (1, 3n 1), (2, 10n + 2), (3, 26n), -27 = a(9)(9 10) At vertex (h, k) = (0, 3) k = 11. Fall Semester Half Year Algebra 1 Guided Notes Bundle Practice Worksheets. Therefore, there is no solution. Work with a partner. y = (0)3 4(0)2 11(0) + 30 = 30 b. y = 3(-1)2 + 6(-1) 1 The population of Town A in 1970 was 3000. -4 = -36a You can solve Algebra 1 Big Ideas Math Textbook Questions easily by referring to our High School BIM Algebra Answers provided. The error is in the first line of the solving for a. System A: REASONING Question 16. Given the x-intercepts (-8, -3, 0) use the intercept form: ERROR ANALYSIS The revenue from calculator sales is given by the function R(n) = (unit price)(units sold), or R(n) = (120 6n)(80 + 8n), where n is the number of $6 price decreases. Answer: Copy and complete the table. x = (-5+1)/2 = -2 ax2 = -2 Answer: Question 3. USING TOOLS x 4 = 0 or x + 2 = 0 Since the second differences are constant, then it is quadratic. Answer: f(x) = ax2 + bx + c 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? Can you find the axis of symmetry when a = 0? b. vertical shift of 5 units downward Find another point on the parabola. -36 = a(-1 + 3)(-1)(-1 2) r(-x) = -6(-x)2 + 5 The 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. After how many seconds does the egg hit the ground? The axis of symmetry is -3 x = -6/6 r(-x) = -6x2 + 5 Graph the axis of symmetry x = -9 + 3/2 = -3 a vertical stretch by a factor of 2 Question 33. Answer: Question 32. Draw the isosceles triangle shown. What changes would improve it? Question 7. Now use the function to find the y-coordinate of the vertex Substitute the x-coordinate to the function to find the y-coordinate which is the maximum or minimum value. x = -1.5 does not make sense in the context of the problem The vertex is at (h, k) and The main difference between the two graphs is that the graph of the given function is the graph of f(x) = x2 translated down by 7 units. Answer: Any quadratic function can be written in vertex form. Question 9. f(x) = \(\frac{2}{5}\)x2 4x + 14 How does the value of h affect the graph of y = a(x h)2? d. The range implies that the parabola opens downward and the y-coordinate is 4. Domain: 10 x 40 Answer: The width is the distance between the 2 x-intercepts Which is different? Answer: Thus g is an even function, d. The sum or difference of two odd functions is odd. x2 + 8x + 5 Given function Answer: Question 28. The axis of symmetry is x = -3. b = 9 a If x = 1 -3(1) + 4 = 1 f(x) = 2x2 4x p(x) = \(\frac{1}{2}\)(x + 1)2 1 y = \(\frac{7}{8}\)x + \(\frac{3}{2}\) Graphing Quadratic Functions Step 2: y = -2x(x2 10x + 25) USING TOOLS In Exercises 3336, use the minimum or maximum feature of a graphing calculator to approximate the vertex of the graph of the function. The axis of symmetry is at x = -b/2a How can factoring help you compare the parabolas? Answer: Question 9. f(x) = \(\frac{1}{2}\)x2 3x 4 f(x) = 5x2 + 10x 3 Answer: 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. The graph of h(x) is a vertical shrink by a factor of 1/3 of the graph of f(x) Solve linear equations with variables on both sides. g(x) = f(x 1) x = -b/2a Rewrite r(x): x-intercepts: -2 and -5 a(-x) + b(-x) + c = ax2 + bx + c y(0) = (0 2)(0 + 2) = -4 Label the vertex, axis of symmetry, and x-intercepts. Answer: The cable between two towers of a suspension bridge can be modeled by the function shown, where x and y are measured in feet. x-intercepts: -1 and 1 Infact, there is no axis of symmetry because the equation will become linear. Verify your answer by solving 0 = 2x2 8x. The formula should be -b/2a y = \(\frac{1}{2}\)x 2 If so, by how much? Question 69. m(x) = 2x2 7x The graph is neither even nor odd because it is not symmetric about the y-axis or the origin. Step 4: Draw a smooth curve through the points. Work with a partner. we have a vertical stretch by a factor of 7 of the parent function y = x2, Question 2. Question 67. Vertex: (6, 0) = -24 + 48 20 Can a linear, an exponential, or a quadratic function represent this situation? f(-x) = f(x) a = -48 and b = 480 g(x) = 5x2 2, Graph the function. In the given function q(x) = \(\frac{1}{2}\)x2 Answer: Question 64. If x = 1 \(\frac{1}{2}\)(1) 2 = -2\(\frac{1}{2}\) y = -(3)(-3) Given the x-intercepts use the intercept form: Question 12. Compare the graph to the graph of f(x) = x2. Question 43. Step 1: Find axis of symmetry: a vertical stretch by a factor of \(\frac{1}{2}\) The equation of a quadratic function is of the form ax2 + bx + c and if a < 0 then the function will have a maximum value of if a > 0 then the function will have a minimum value. Answer: Evaluate the expression when n = 3 and x = 2. Explain your reasoning. The vertex form of the quadratic function is a = 3 The graph is a line so the function is: Function D f(x) = 5(x 3)2 1 3x = 9 or 4x = -12 Graph g. Describe the domain and range. Answer: Question 7. y = -(x + 5)(x 1) y = \(\frac{1}{8}\)(x 4)2 y = 0.25x2 52/3x + 2 Answer: Question 74. Question 10. -36 = a(-6 + 8)(-6 + 3)(-6) (x 1)(x 4) = 0 h = 0 and t = 2.5 sec, Question 1. Big Ideas Math - Algebra 1, A Common Core Curriculum Larson, Ron; Boswell, Laurie Publisher Big Ideas Learning LLC ISBN 978-1-60840-838-2. a vertical contraction by a factor of \(\frac{1}{2}\) and Question 11. -16x2 + 36 = 0 f(x) = a(x h)2 + k x = 2 + (-2)/2 = 0 A cross section of the parabolic surface of the antenna shown can be modeled by y = 0.012x2, where x and y are measured in feet. y = (x 2)(x + 2) Axis of symmetry: x = 3. Answer: A possible answer is a = 1, b = 0, c = 2 Answer: Question 46. Answer: b. Answer: Question 3. f(x) = 2x2 + 1; g(x) = f(x) + 2 Explain how you found the x-intercepts. The graph shows the population of Town B. . Answer: Question 5. REASONING Therefore, the original revenue results in a greater maximum monthly revenue. We can insert a point in the equation to get a = 8, Question 7. Range: {y R: y -25/4} x2 + x 12 = 0 In Exercises 914, plot the points. 0 = -3(x + 3)(x + 1) Question 3. = x + 7x + 10. Thus r(-x) = r(x) Question 29. The guide that KA posted has only 3 chapters. f(x) = \(\frac{1}{15}\) (x 3)(x 13) We also can see that the functions y-intercepts is 123, Answer: The point appears to represent a quadratic function with an axis of symmetry of x = -1. m = 45 t(x) = -5-3/3-1 = -4 -6/-2 = -18/-6.. geometric sequence. x = (p + q)/2 0 = \(\frac{1}{20}\)(3 19(3) + 48) g(x) = -2(x 4)(x + 1) x = 7 x = -(-6)/2 . As a result, the entire solution is incorrect. How to Solve Big Ideas Math Algebra 1 Textbook Questions easily? y = \(\frac{3}{4}\) x2 + 9x 18 Substituting x = 0, the y-intercept is Graph the axis of symmetry x = 3 + (-4)/2 = -0.5 Answer: The behavior of the graph changes at x = 4. Seek the Homework help you might need by accessing our Big Ideas Math Algebra 1 Answers and clear all your queries. x2 + 4x 3x 12 Question 105. Three organizations are collecting donations for a cause. Question 31. The related function is increasing when x < 0, and the zeros are -1 and 1. Essential Question How does the value of c affect the graph of f(x) = -ax2 + c? Since h = -9, the axis of symmetry is x = -9 and the vertex is (-9, 0). f(x) = x(x 6) WRITING Use a graphing calculator to check your answer. Answer: j(x) = 0.75x2 y = -6.2x2 + 4.8x 1 Answer: Question 44. 7/8 = v0/32 1 = a . Question 18. The main difference is that the graph of the given function opens wider than the graph of f(x) = -4x2. The constant 25 represents the initial height of 25 feet. Describe the domain and range of the function. Free Easy Access Student Edition - Common Core High School. f(x) = (x 8) + 8 Thus the range is (-, 18]. At (2, 5): 0 = a(2) + b20) + c (2)0 f(x) = a(x h)2 + k In Exercises 6972, write the cubic function represented by the graph. Answer: f(x) = -2x2 + 8x + 24 Answer: y = 3(1/3)2 2(1/3) b. 3(-2)2 + (-2) 2 Then write the function. = f(b) f(a)/b-a x(x 1) 3(x 1) = 0 Comparing Speeds Answer: Waterfall 1 sends water the farthest. How are the graphs in Monitoring Progress Questions 1-8 similar? To determine is function odd, even, neither, you should replace x with -x. Answer: Question 14. When is each function decreasing? THOUGHT PROVOKING 3x2 + x 2 y = a(x p)(x q) vertex: (1, 8); passes through (3, 12) Answer: Question 15. Let f(x) be an even function. y = -2x2 + 6x + 8 Graphing f(x) = ax2 + bx + c, p. 432 Also, you can refer to the covering Questions from Practice Test, Chapter Test, Cumulative Practice, Performance Test, etc in this Chapter 8 Big Ideas Math Answer Key. x = \(\frac{b}{2a}\) Then find the value. Answer: Thus the points represent a linear function. a. a vertical contraction by a factor of \(\frac{1}{2}\) Comparing Speeds x 1 = 0 or x 3 = 0 or x + 3 = 0 Thus maximum height is 18 feet and after achieving it the softball hits the ground. Answer: Question 12. = -12 + 1 Plot the corresponding points: (-9, 0), (-3, 0), (0, 0) Use the other point (10, 1.4) to find the value of a ERROR ANALYSIS In Exercises 43 and 44, describe and correct the error in finding the zeros of the function. Answer: Question 94. Does changing the value of p change the y-intercept? You can click directly from the PDF to go to resources on the Khan Academy website. Explain your reasoning. y = 2(x+2)(x + 2) How did you use the structure of the equation in Exercise 85 on page 457 to solve the problem? g(x) = 2x2 4x web pages Yes, he is correct. = -26. Answer: f(x) = \(\frac{1}{4}\)(x 6)2 Question 27. Answer: = 36 72 + 13 Answer: Question 93. -2 = a(8 6)(8 10) p(x) = -40-(-16)/3-1 = -12 Waterfall 1 h = -3.1d2 + 4.8 Answer: Waterfall 3 follows the narrowest path Question 3. Question 27. In Exercises 4548, let f(x) = (x 2)2 + 1. Vertex form is Answer: Question 58. Question 7. Question 7. y = -2x2 + 6x + 8 Plot the points (3, 0) and (-4, 0) g(-x) = 3(-x)2 Question 41. y = 45x. a. First difference: 49.7, 63.9, 78.1 h(x) = \(\frac{1}{4}\)x2 + 3x + 1 Answer: q(x) = -(x + 4)2 + 7 If not, explain why. x + 3 = 0 or x + 1 = 0 (x 1)2 is always , so the range is y 6, Question 11. f(4) = f(3) + f(2) = 2 + 1 = 3 x2 (x 1) -9(x 1) = 0 Answer: The axis of symmetry is 2 Answer: Question 70. y = x2 17x + 52 Answer: Answer: As (119, 0) lies on the function, putting the values in function we get bx, Answer: 0 = x This will help you recall the information while taking a test. Question 102. Describe the transformation from the graph of f to the graph of g. Then graph f and g in the same coordinate plane. Rewrite p(x): 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. -27= -9a Since the first differences are constant, then it is linear. y = -16(0) + 36 What are some of the characteristics of the graph of a quadratic function of the form f(x) = ax2? The points from a straight line. x(x + 4) 3(x + 4) = 0 VOCABULARY f(1) = -3(1)2 + 6(1) + 9 = 12 g(x) = 8x2 8x + 6 g(x) = |x 2| + 5 ANALYZING RELATIONSHIPS Therefore there is 1 solution. x = -6 or 6 or 11, Question 30. y = abx Question 73. w(x) = 5x 2x + 6 = 0 = -16(1)2 + 32(1) + 2 Question 3. Question 27. Answer: f(x) = 3x2 27 The range is [-9, +), Question 16. Find the average rates of change of each function for each 1-hour interval from t = 0 to t = 6. Can the horse clear a fence that is 3.5 feet tall? f(x) = 3x2 2x x = 1, 4, Question 8. Answer: The formula for axis of symmetry is incorrect. The domain is the set of real numbers. You will find the Algebra 1 Big Ideas Math Answers of extreme help and covers questions from Practice Tests, Chapter Test, Cumulative Practice, etc. = -4 + 8 Direct link to Donna Brink's post Is there only 3 chapters , Posted 5 years ago. How can you find the vertex of the graph of f(x) = ax2 + bx + c? Domain: 15 x 45 The first differences are: -8, -16, -24 Additional Resources x2 4x 13x + 52 = 0 The axis of symmetry is given by x = (-3 + (-1))/2 = -2 f(x) = -(x + 2)2 + 6. range: y 10 The x-intercepts are 5 and 3 We observe that the two graphs have the same domain, range, axis of symmetry and are both parabolas. x = -b/2a f(x) = a(x + 2)(x + 5) Which graph does not belong with the other three? y = 3(-1/3)2 + 2(-1/3) The y coordinates are y = 0 Answer: Question 32. f(x) = (x + 5)(x2 4) Answer: 14 day loan required to access PDF files. 5 = a(6 1)(6 7) f(x) = x + 12x + 35x. Given, y = 2(x-2)(x-2) Does changing the value of p change the x-intercepts? y = ax + bx You are playing tennis with a friend. How do you know that (-4, 2) is not the vertex? i. a horizontal shift of 1 unit to the left REASONING What do you notice about the x-coordinate of the vertex of each graph? Let f, h be even function. 5x2 9 Answer: a = 5 Chapter 5 Practice Test Practice test: Big Ideas Math Algebra 1 - Chapter 5: Solving Systems of Linear Equations Week {{::cp.getGoalWeekForTopic(5, 11)}} Ch 6. The maximum value is attained at vertex. p = 6 and q = 10 t = 2, Question 22. Open Access Materials y = 0 4 Question 7. Answer: Step 2: Graph the axis of symmetry: Write a function of the form y = ax2 + bx whose graph contains the points (1, 6) and (3, 6). Answer: on December 27, 2021, There are no reviews yet. Question 29. b. Answer: 2x Domain is (-, +) a = -2 and b = 8 Notice that the y-values are symmetric with respect to the point (0, 0). Describe the domain and range of the function. After how many seconds does the pinecone hit the ground? y = (x + 5)(x 3) Answer: From the table, a vacation of 9 days will amount to the price. Answer: Answer: Question 33. \(\frac{a}{4b}\) Question 35. A store sells custom circular rugs. Explain. Parabolas have several recognizable features that characterize their shape and placement on the Cartesian plane. . (-1, 5), (2, -1), (0, -1), (3, 5), (1, -3) b. Question 39. A parabola passing through 2 points give two linear equations with 3 variables that need to satisfied. MODELING WITH MATHEMATICS Consider the functions represented by the tables. So, the vertex is (4, -1) y = 2(-2)2 + 8(-2) + 3 Do you have it aligned to big ideas course 1? Find the x-coordinate where y = 0 which is at x = 90 f(x) = ax2 + c Answer: t1 = 0 or 1 f(x) = \(\frac{1}{2}\)x2 + 1 The graph is an exponential decay so b < 0 which is Function C. Answer: The cables between the two towers of the Tacoma Narrows Bridge in Washington form a parabola that can be modeled by y = 0.00016x2 0.46x + 507, where x and y are measured in feet. f(x) = -1/2(x + 8)(x + 2) -14 = a(0 + 3)2 + 5 f(x) = (x 2) + 1 The graph is symmetric about the y-axis. y = 3x2 + 6x 1 The x-intercepts are 4 and -2 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. y = -(x + 1)2 3 Question 37. Find the number of solutions to a linear equation. R(n) = (120 6(5))(80 + 8(5)) = 10800 f(9) = f(8) + f(7) = 21 + 13 = 34 Point 1: (0, 3) Question 25. How wide is the satellite dish? Find the axis of symmetry of the graph of the equation y = ax2 + bx + c when b = 0. = 12 f(x) = x2 4x + 3 4 unit shift downward, Question 21. Answer: Answer: Question 32. ERROR ANALYSIS Explain. Answer: The other equation asks for the y-value of the vertex. The common ration is 1.11 so b = 1.11 Which function is represented by the graph? Graph f(x) = g(x) 3 g(x) = 3x2 = 9 + 5 A cross section of a birdbath can be modeled by y = \(\frac{1}{81}\)(x 18)2 4, where x and y are measured in inches. Answer: Explain your reasoning. Answer: Question 84. . a = \(\frac{3}{4}\) and b = 9 Essential Question What are some of the characteristics of the graph of a quadratic function of the form f(x) = ax2? x = -5 or x = 6, Question 42. Answer: Answer: c. Use the graph of y = 2x2 8x to find its x-intercepts. Then h(t1) = 0 and t1 > 0 Question 79. Answer: To help determine the shape of the graph, find the points between the zeros and plot them. -4 = m 2 Question 43. Aliz CarrreEnvironmental Anthropologist. 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 8 units. WRITING -2, -6, -18, -54, . Therefore the function is ERROR ANALYSIS g(x) = 6x3 + 30x2 36x Comparing x-Intercepts with the Vertex The distance traveled in t minutes is y miles. Answer: In what year were the populations about equal? We are given that (119, 0) lies on the graph. y = -2(2)2 + 8(2) + 24 h(x) = (x 2)2 + 4 Answer: Graph the function. Let a = 1 The y-coordinate of vertex is y(0) f(x) = a[x (-2)][x (-5)] The cross section of a satellite dish can be modeled by the function shown, where x and y are measured in feet. Question 25. Question 13. 3x2 27 = 0 Given the x-intercepts (-8, -2) use the intercept form: Describe how the graphs of the two equations are related. t1 = 1s. So, the vertex is (0, -48) They score points based on the number of hits per shot. g(x) = f (x + 5) Answer: a = 4 and b = -3 Monitoring Progress 26: Monitoring Progress 27: Monitoring . Algebra Big Ideas Math: Algebra 1 Student Journal 1st Edition ISBN: 9781608408528 HOUGHTON MIFFLIN HARCOURT Textbook solutions Verified Chapter 1: Solving Linear Equations Page 1: Maintaining Mathematical Proficiency Section 1.1: Solving Simple Equations Page 6: Extra Practice Section 1.2: Solving Multi-step Equations Page 10: Extra Practice 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. Answer: Question 5. f(x) = a(x (-3))(x 0)(x 2) x intercepts of parabola in intercept form are given p = 2 and q = 5 Find the domain, range, and zeros of the function. f(x) = (x + 2)(x 3) The x-coordinate of the vertex is 0 x = -1 or x = 1. MODELING WITH MATHEMATICS Answer: f(x) = a(x p)(x q)(x r) The second differences are: -8, -8 vertex: (-5, -1); passes through (-2, 2) = -2(-2)2 4(-2) + 3 (-2, 8), (-1, 0), (0, -4), (1, -4), (2, 0), (3, 8) Answer: Answer: Let f, h be odd function. Estimate the maximum height of the arrow. Given, There are even more practice exams available in Big Ideas Math Algebra 1 - Chapter 6: Exponential Functions & Sequences. In Exercises 1926, find the zeros of the function. In Exercises 3742, use zeros to graph the function. Substitute x = 18 for 18 mph Compare the speeds of the three cars. f(x) = 4(x 2))2 + 3 y = (x 4)(x + 2) f(x) = (x + 2)(x 6) Answer: x = 6, h = 6 x = -10/10 = -1 Consider the graph of the function f. Use a graph to justify your answer. The axis of symmetry is -1/3 The graph of g(x) is a translation left 5 units of f(x), The kicker kicks closer to his goal line the second time. y = x3 x2 9x + 9 System B: 0 = -2x2 + 6x + 8 Explain your reasoning. Answer: Answer: So, the vertex is (-2, -1) How far from each tower shown is the lowest point of the cable? Range: {y R : y -36}, Find the zero(s) of the function. Answer: Question 4. Let the year x represent the independent variable. Answer: Question 14. Answer: Question 3. bx, where b is the common ratio. The highest point on the parabola is (0, -5). MAKING AN ARGUMENT y = 2(x + 1)2 3 Direct link to Adam Ashcraft's post Wow, these comments were , Posted 5 years ago. . Thus the tentative equation of the function that represents the given table of values 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 f(x) = -(x + x + 5x + 5) Therefore the equation of the quadratic function whose graph is given The consecutive y-values have a common ratio of 5. (b) Predict which account will have a greater balance after 10 years. y = -(-2)2 4(-2) + 2 g(-x) = f(-x) + ah(-x) System F: h(x) = x(x2 1) Function is even if f(-x) = f(x) and function is odd if f(-x) = -f(x) 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. Since (2, -2) lie on the graph, x 6x 5. y = 2(5/2)2 10(5/2) + 13 = 1/2 1 Answer: Question 85. . 0 = 4a + 8 The third graph from the left does not belong to the group. Answer: Answer: If c changes however, then the vertex will also change. Given, ASHLEY LAWRENCE. No, because 500 not a multiple of 45 as shown above. f(x) = (x + 7)(x + 5)(x) = -(-0.37)/2(0.000098) = 1888 REASONING Explain. f(-3) = (-3)2 + 6(-3) 27 = -36 The shot also passes through the point (10, 1.4). f(x) = a(x 1)2 + 8 f(8) = f(7) + f(6) = 13 + 8 = 21 Range: {yR:y-9} There are also two versions of a review for the tests.All four tests cover Function Families (Constant, Linear, Quadratic, Absolute Value) and Transformations of those functions. 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. 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. Explain. g(-x) = -f(x) + a(-h(x)) = -g(x) The graph of f(x) = x2 is narrower than the graph of g(x) = x2 when a > 0. What is the maximum area of the outside enclosure in terms of k? b = 9 (-3) Explain how you can tell whether a quadratic function has a maximum value or a minimum value without graphing the function. Answer: Thus, parabola is of the form f(x) =ax2 f(x) = \(\frac{1}{5}\)x2 5x + 27 The parabola opens up, and the vertex is (0, 3). Sketch the graphs of y = 2x2 8x and y = 2x2 8x + 6. WRITING Section 8.1 Since the vertex is located at the axis of symmetry, we can find the y-coordinate by substituting x = 2 Question 5. Is the x-intercept of the graph of y = x2 always 0? Construct a table from x = 0 and x = 3 Answer: Question 56. Let x represent the number of decades since 1970. In these eSamples you will be able to view a sample chapter from each book as well as the Table of Contents, Front Matter, and more! n(x) = \(\frac{1}{3}\)x2 5 r(x) = 4(x 1)2 5 x(x 1) = 0 y = 3x2 + 2x Answer: Question 24. Answer: y = 0.5x2 + \(\sqrt{2x}\) x 3 when b = 0 Answer: The vertex is at (7, 10580) Answer: Explain the process you used. f(6) = \(\frac{1}{2}\)(6) 6(6) + 10 y = a(x h) + k Explain your reasoning. 5.0 (3) $99.00. f(x) = x 16x + 64 + 8 (4y + 2)(4y 2) The cross section of a spotlight can be modeled by the graph of y = 0.5x2, where x and y are measured in inches and -2 x 2. WRITING y = -(x 6)2 5 How can you describe the graph of f(x) = a(x h)2? f(x) = 3(x + 1)2 We note that both graphs are parabolas and have the same range and axis of symmetry. Label the vertex, axis of symmetry, and x-intercepts. Answer: a. y = (x 3)2 Question 27. MODELING WITH MATHEMATICS y = -2(x-5) + 8 USING TOOLS Answer: Question 72. As c increases, the graph will be translated up and thus the vertex will go closer to the upper point A. (a) Compare the account balances by calculating and interpreting the average rates of change from t = 2 to t = 7. 3x2 12x + 12 = 0 The first differences are: 15, 25, 35 f(x) = \(\frac{1}{2}\)x2 2; g(x) = f(x) 6 2x = -6 Vertically stretched by a factor of 2 g(x) = f(x) 4 Answer: Question 99. f(1) = h(1) = 1, Graphing f (x) = ax2When a < 0, p. 421, Section 8.2 Answer: Question 28. f(12) = f(11) + f(10) = 89 + 55 = 144 Given, Thus the correct answer is option C. Question 7. Question 47. Which birdbath is deeper? a. What is the maximum height of the pumpkin? Answer: Question 24. From the graph, the x-intercepts are 1, 3, 6. x = \(\frac{25}{2}\) From the graph, the x-intercepts are -3, 0, 2 x = -b/2a Answer: Question 14. Tell whether the points appear to represent a linear, an exponential, or a quadratic function. Answer: Use any point say (1, -4) to find the value of m f(x) = 2x-1 USING STRUCTURE In Exercises 8790, match the function with its graph. Answer: Answer: Question 28. Using Your Book . h = 4, k = 8 Answer: b. a vertical shift of 1 unit downward Answer: a. The function is odd if it satisfies: h(x) = -x2 Answer: Question 31. Answer: Answer: Range: y 8 4a + 6 = 2 Answer: 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 x = 2 Write a quadratic equation whose graph models the shape that appears. The graph shows the numbers of donations collected by Organization C. x-intercepts: 1 and 9 Use the recursive rule until the term is greater than 100 where it is not included: Describe the domain and range of the function. Question 35. They are listed in the following fashion. Answer: Question 10. y = (1)(x 0) + 3 Answer: Axis of symmetry: x = -4 Show your work. Question 5. decreasing? -x2 + 4x + 1 Answer: Question 28. f(x) = a(x 1)2 + 2 Without graphing, describe the graph of each function. the Range is all real numbers greater than or equal to -3, Question 2. The x-coordinate of the vertex is -3 Direct link to mistie van noort's post Do you have it aligned to, Posted 4 years ago. If x = 3 -3(3) + 4 = -5 y = (x + 3)(x 3) The function p(x) = \(\frac{1}{2}\)(x + 1)2 1 involves: Answer: Question 8. a. a vertical stretch by a factor of 2 g(x) = 2x2 + 3, Question 10. Describe the domain and range. y = -6.2x2 + 4.8x 1 Question 90. -4x2 + 2x 6 The domain is all real numbers n = 480/2(-48) = 5 Explain. What is the height of the cable above the water at its lowest point? The graph is shifted to the right by 2 and up by 5. a. Request Samples and Digital Access. Answer: Find the axis of symmetry and vertex: Work with a partner. f(3) = f(2) + f(1) = 1 + 1 = 2 Question 31. Answer: Axis of symmetry: x = 2 p(x) = -5x2 10x 2 Answer: Question 48. Vertex: (-2, 0) x = 2 The vertex is (-2, 0). Answer: we have a vertical stretch by a factor of 6 of the parent function y = x2. f(x) = -2(x 4)2 8; g(x) = -f(x) Which of the intervals in Question 3 describes the value of a? 1. f(-1) = -2(-1)2 4(-1) + 30 = 32 Also, you can refer to the covering Questions from Practice Test, Chapter Test, Cumulative Practice, Performance Test, etc in this Chapter 8 Big Ideas Math Answer Key. If x = 4 -3(4) + 4 = -8, Question 3. where a = -0.005 and b = 0.17 Vertex is (2, -3) Answer: h(x) = 8x2 8 -1 Question 9. Therefore the data must represent an exponential function with a base of 2. The range is y 4 An office supply store sells about 80 graphing calculators per month for $120 each. The function h(x) = 2x 3 involves a vertical stretch by a factor of 2 and a 3 unit downward shift of the function f(x) = x2, Question 2. PROBLEM SOLVING y = (x 5)(x 3) b = -2ahx The Big Ideas Math: Modeling Real Life program comes with built-in parent support. 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