Answer: b. Therefore the equation of the quadratic function whose graph is given To help determine the shape of the graph, find the points between the zeros and plot them. In Exercises 36, find the x-intercepts and axis of symmetry of the graph of the function. Question 33. Finding x-Intercepts of Graphs y = a(x + 2x 8) q(x) = x2 1 The range is y 4 The graph of an odd function is symmetric about the origin. y = -x2 + 4x + 12 Use the vertex form: f(-x) = \(\frac{1}{2}\)x web pages Since (2, -2) lie on the graph, The axis of symmetry is y = 36 represents 36 ft, the initial height the apple was dropped. Question 43. f(x) = a(x 1)(x 7) h(x) = 8x2 8 After how many seconds does the pinecone hit the ground? Now we have to substitute x = -2 in the above expression h(x) = \(\frac{1}{2}\)x2 + 7x 4 h(x) = 3x 6 Describe the possible values of a. The consecutive y-values have a common ratio of 5. The y-intercept is (0, 36) 2. Answer: A = \(\frac{1}{2}\)(12 4x + 12)(x + 2) Getting helpful and educational math answers and solutions to high school Algebra 1 exercises could be the key to . Step 1: The x-intercepts are -9 and 3. Solving a and b, a = 1.5, b = -0.5 a. Then find the value. Vertex: (-2, 0) Since the leading coefficient is negative, the function has a maximum value. WRITING y = a . Answer: Question 96. Since f, h are even functions. The parabola opens up, and the vertex is (0, 3). The graph shows the amounts y (in dollars) that a referee earns for refereeing x high school volleyball games. 4r 36s. For r(x): Click the image below to download the PDF Guide. a. f(x) = (x2 1)(x2 4) f(x) = 3(x)(x 10) The graph is shifted to the right by 2 and up by 5. Just tap on the chapter you need as a part of the preparation and get better grades in your exam. point 2: (-2, -6). Answer: Step 3: Compare the graph to the graph of f(x) = x2. Answer: Tell whether the table of values represents a linear, an exponential, or a quadratic function. Question 15. f(x) = 1(x 4) + 8 Question 42. y = (x + 3)(x 3) f(x) = -x2 + 4x + 2 5.0 (3) $99.00. f(x) = a(x (-1))(x 1)(x 2) g(x) = 2x Thus the function is even. y = -2x2 + 6x + 8 Question 5. Direct link to 054775's post Great product.but it w, Posted 5 years ago. How many calories are in the burger that contains 12 grams of fat? Answer: You will find the Algebra 1 Big Ideas Math Answers of extreme help and covers questions from Practice Tests, Chapter Test, Cumulative Practice, etc. In what year were the populations about equal? r(x) = \(\frac{1}{4}\)(x + 10)2 Answer: Is your friend correct? Question 43. Answer: a. n = 280/2(-20) = 7 Answer: Which function is represented by the graph? Step 2: h(x) = x3 6x2 + 5x y = a(x-p)(x-q) Answer: MAKING AN ARGUMENT x = 4 or x = 13, Question 26. Answer: Answer: Question 14. b. Write a function of the form y = ax2 + bx whose graph contains the points (1, 6) and (3, 6). The third graph involves an exponential function. The function g(x) = \(\frac{1}{2}\)x2 involves a reflection about the x-axis and a vertical contraction by a factor of \(\frac{1}{2}\) of the function f(x) = x2, Question 3. Then write a function that models the data. The Big Ideas Math: Modeling Real Life series comes with two options of accelerating students, the Advanced Pathway and the Compacted Pathway. In Exercises 6168, use zeros to graph the function. 26, 18, 10, 2, -6, . On the other hand, for the important concepts they just go through very quickly, and do not offer enough practice. To help determine the shape of the graph, find the points between the zeros and plot them. b(x) = 2.5x2 If c changes however, then the vertex will also change. Answer: x = -10/-10 = 1 Answer: A = x 2ax + a Given the x-intercepts use the intercept form: Work with a partner. Answer: a. 7 unit shift upward of the parent function y = x, Question 20. They score points based on the number of hits per shot. -36 = a(-1 + 3)(-1)(-1 2) Vertex: (6, -5) 9a 1 = 2 f(-x) = \(\frac{1}{2}\)(-x) a = -300/3600 = -1/12 Question 2. Vertex is (1, 4) Answer: Answer: Question 15. You are standing 30 feet from the net, which is 3 feet high. Answer: Explain your reasoning. In both functions, y represents vertical height (in feet) and x represents horizontal distance (in feet). . Answer: Compare the graph to the graph of f(x) = x2. b. In the given function q(x) = \(\frac{1}{2}\)x2 ANALYZING GRAPHS In Exercises 2123, use the graph. Then find the value. Question 6. 5 4 9 5 not an arithmetic sequence a. 6x = 2 Work with a partner. At 1990 (t = 2): y = 5000 Area of trapezoid = \(\frac{1}{2}\)(b1 + b2)h g(x) = f (x + 5) If x = 2 \(\frac{1}{2}\)(2) 2 = -3 a = 6 Question 1. c. The range implies that the parabola opens upward and the y-coordinate is -6 Is your friend correct? x = 90 meters. p(x) = f(x) 3 g(x) = 6x(x2 + 5x 6) x = 7 b. y = 2x2 8x + 8 g(x) = \(\frac{1}{4}\)x2 To find the value of a, substitute the x and y values of the point on the parabola (6, 5) Question 41. -4x2 + 2x 6 f(x) = 5(-1)2 + 10(-1) 3 There are numerous benefits that come by referring to Big Ideas Math Algebra 1 Answers. = 2 What is the initial height of the arrow? Answer: Question 22. Answer: The Algebra 1, Geometry, and Algebra 2 program purposefully integrates five key strategies proven to have the highest impact on student achievement. Explain your reasoning. = -6(2)2 + 24(2) 20 t . Parabolas A and B contain the points shown. Given the x-intercepts use the intercept form: How did you choose the model? y = 5x(x + 2)(x 6) y = 2x)2 8x + 4 y = \(\frac{1}{2}\)x2 + 7x 4 If x = 4 -3(4) + 4 = -8, Question 3. \(\frac{7}{3}\). f(x) = \(\frac{1}{2}\)x HOW DO YOU SEE IT? a. Answer: Chapter 1 Solving Linear Equations Chapter 2 Solving Linear Inequalities Chapter 3 Graphing Linear Functions Chapter 4 Writing Linear Functions b. y = (x + 3)2 Question 18. Answer: Answer: Question 12. y = 3(-1/3)2 + 2(-1/3) Question 3. Find the domain, range, and zeros of the function. f(x) = (x 4)(x 6) f(x) = -x 11x + 24x. Graph the axis of symmetry x = 3 + (-5)/2 = -1 y = 0.5x2 + \(\sqrt{2x}\) x 3 In Exercises 1318, graph the function. y = -(x 6)2 5 Width of arch = 500 (-500) y = 1.5x 0.5x. The function f(t) = -16t2 + v0t + s0 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). Question 1. The function g(x) = -16x2 + 300 represents the height (in feet) of your friends ball after x seconds. y = -0.4x2 Thus maximum height is 18 feet and after achieving it the softball hits the ground. f(x) = \(\frac{1}{2}\)x2 + 4x + 3 y = x2 9 Become pro in the Algebra Concepts and clear the assessments or get the Homework help you might need using the BIM Textbook Algebra 1 Answer Key. x2 17x + 52 = 0 ax2 bx + c = -ax2 bx c Suppose the initial height is adjusted by k feet. f(x) = (x 8) + 8 ax12 + b1 + c = y1 c y = -2(x 2)(x 5) y = x + 5 a = -2, b = 8 Question 51. Answer: d(x) = \(\frac{1}{5}\)(x 5)2 HOW DO YOU SEE IT? we have a vertical stretch by a factor of 7 of the parent function y = x2, Question 2. b. Substituting x = 0, the y-intercept is The textbook market has been cornered by a few big . y = -2(x 2)(x 10) When does the firework explode? x(x 4) 13(x 4) = 0 x = 2 Answer: Question 28. . Question 3. = 4/2(1) = -2 r(-x) = -6x2 + 5 A kicker punts a football. Write an equation for the function in vertex form and in standard form. (2)0 Answer: Question 2. f(x) = a(x 59)2 + 300 (x 1)(x 9) = 0 Answer: Question 20. Question 5. Question 7. Answer: Mathematically proficient students try special cases of the original problem to gain insight into its solution. a = 1/2. The graph of a quadratic function passes through (3, 2), (4, 7), and (9, 2). (-2r + 6s)(-2r 6s) Answer: Question 5. In the given function h(x) = 2(x 4)2we have College Algebra (10th Edition) Sullivan, Michael Publisher Pearson ISBN 978--32197-947-6. Answer: Answer: = 4 Consider the function f(x) = x2 + 4. Use the zeros and the other point given to write a quadratic or cubic function represented by the table. Question 3. Substitute either intercepts to find a: Let g(x) = f(x) + ah(x) Axis of symmetry is x = -2 Axis of symmetry is x = 0 q(x) = \(\frac{1}{2}\)x2 + 6 In Exercises 3136, match the function with its graph. g(x) = (x + 1)2 7 y = -1/3 -2 = a(1) y = -3x + 5 System D: Answer: y = x3 4x2 11x + 30 In the given function q(x) = 7x2 Essential Question How does the value of c affect the graph of f(x) = -ax2 + c? This means that the vertex of the parabola is (0, 0) b. g(x) = x(x2 1)(x2 4) Woodrow Wilson high School. In Exercises 4556, write a quadratic function in standard form whose graph satisfies the given condition(s). Now substitute 1888 for x in the equation to find the y-coordinate of the vertex. Describe the domain and range of the function. g(x) = 5x2 3 + 1 Function is even if f(-x) = f(x) and function is odd if f(-x) = -f(x) Answer: Question 48. Answer: Answer: Question 4. Question 8. = -2(4) + 8 + 3 Thus the function is odd. (-2, 8), (-1, 0), (0, -4), (1, -4), (2, 0), (3, 8) g(x) = (x 1)(x 3)(x + 3) From t = 2 to t = 3: Answer: y = 3(-1)2 + 6(-1) 1 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. Answer: Question 32. Step 2: range: y 5; passes through (0, 2) y = 36 Explain. The axis of symmetry is x = 2. 6 = 2a Thus the range is (-, 18]. The graph of an even function is symmetric about the y-axis. c. Use the graph of y = 2x2 8x to find its x-intercepts. g(x) = f(x) 6 For the given graph the x-intercepts are 1 and 7. The function g(x) = f(x) + 2 involes additiion of 2 to f(x) therefore g(x) involes a 2 unit shift upward of the graph of f(x). Explain your reasoning. g(x) = \(\frac{1}{2}\)x2 Given the x-intercepts (-8, -3, 0) use the intercept form: x(x 1) 3(x 1) = 0 The width is the distance between the 2 x-intercepts Answer: There is a common ratio which is 1/2 Answer: Question 19. The graph of f(x) = x2 is narrower than the graph of g(x) = x2 when |a| > 1. x = 0 or x 1 = 0 a = -1, Question 60. Step 4: Draw smooth curve through the points. Vertex is (-3, -23) y = 2(x+2)(x + 2) r(x) = -6x2 + 5 The other equation asks for the y-value of the vertex. y = x3 4x2 11x + 30 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. b. Let the speed x represent the independent variable. g(x) = x2 + 6x + 5 Odd, Question 12. Answer: = 12 a. 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. Answer: Question 99. x = 24/2(4) = -3 The y coordinates are y = 0 Therefore the vertex of the parabola is at (-1/2, 8) Question 3. If so, by how much? y = \(\frac{7}{8}\)x + \(\frac{3}{2}\) Let the time t represent the independent variable. Answer: Question 34. f(x) = a(x 0)(x 10) Question 10. f(x) = a(x + 2)(x + 5) USING TOOLS Answer: Also consider: . g(-x) = af(-x) Answer: y c if if a < 0 Answer: Question 64. Many of the things we do as educators have a positive effect on student learning, but which ones have the greatest impact? Question 13. WRITING USING STRUCTURE CRITICAL THINKING Question 1. The range implies that the parabola opens upward and the vertex is at (0, 3) Using Your Book . Then we know that -1 < a < 0. q(x) = \(\frac{9}{2}\)x2 Question 19. -14 = a(0 + 3)2 + 5 Common Core Assessment Practice for Mathematics. In Exercises 712, graph the quadratic function. f(t) = -16((t \(\frac{11}{4}\)) \(\frac{133}{16}\)) h(x) = \(\frac{1}{2}\)(x + 4)2 2 Let f, h be even function. x = 7, Question 24. Answer: Question 3. f(x) = 1/3(x + 5)2 1. Answer: Answer: -72 = -12a f(x) = 2x2 + 1; g(x) = f(x) + 2 p(x) = -5x2 10x 2 b2, Then write the function. 4a = -8 Compare the graph to the graph of f(x) = x2. y = 9 Label the vertex, axis of symmetry, and x-intercepts. Answer: Consider function g in Example 3. x 4 = 0 or x + 1 = 0 Question 15. Explain how you found the x-intercepts. Answer: In Exercises 5760, write the quadratic function represented by the graph. Answer: Open Access Materials h(x) = 2x2 + 3 Answer: b. C? x = -3 f(x) = -2(x 4)2 8; g(x) = -f(x) Answer: Question 8. Given, Answer: f(x) = 2(x 1))2 + 1 3x 9 = 0 or 4x + 12 = 0 The x-intercepts are -3 and 4. Since a < 0, maximum value exists. First we will graph the function and find the axis of symmetry a = 4 and b = 24 h(x) = -x2 4 There is no real zero when the graph does not cross/touch the x-axis. Answer: In Exercises 36, find the vertex, the axis of symmetry, and the y-intercept of the graph. (0, 0), (1, 1), (2, 5) The range contains all possible y values that the function can take on and we note in this case that the function only takes on values less or equal to 13. Answer: y = \(\frac{1}{2}\)(x 1)2 + 3 Write an equation that represents g in terms of x. 4 = -8a a. Given, Answer: 5. g(x) = x2 + x 12 Two intercepts are given (3, 0) and (13, 0) In Exercises 58, tell whether the points appear to represent a linear, an exponential, or a quadratic function. \(\sqrt [ 5 ]{ 243 }\) What are the x-intercepts of the graph of y = ax2 + bx? Domain: All real numbers A store sells custom circular rugs. Explain. Answer: Given, The table shows the distances d (in miles) the student travels in t minutes. In the given function g(x) = \(\frac{1}{2}\)(x 1)2 + 1 we have Question 23. Step 1: The x-intercepts are 3 and -5. axis of symmetry equation is x 0.5, Question 8. y = a(x + 4)(x 2) Using a different revenue model, the store expects to sell five more calculators for each $4 decrease in price. c tell us the intercept of graph. c = 0 The function is neither odd nor even when a, b and c are non-zeros x = -b/2a Make sure your notes are visually neat for easy recall. n(x) = -(x + 4)2 + 2 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. A possible answer is: a = 1, b = 2, c = 3. f(x) = \(\frac{1}{2}\)x2 + 1 Substituting x = 0, the y-intercept is y = -2(2)2 + 8(2) + 24 notice that h(-x) is not equal to -h(x) or h(x) -(-2)2 + 4(-2) + 1 Therefore the data must represent an exponential function with a base of 2. Answer: g(x) = f(x) + h(x) How to Solve Big Ideas Math Algebra 1 Textbook Questions easily? Answer: Question 61. Question 7. x = \(\frac{-b}{2a}\) f(x) = (x + 2)(x 3) Question 9. Answer: Question 70. y = a(x + 2)2 + k f(x) = \(\frac{1}{9}\)(x 30)2 + 25 B? The average rates of change are the rate of increase of the population from 1990 to 2010. x = -1/3 y intercept is c = 13. What do you notice about the average rates of change when the function is increasing? Axis of symmetry: x = -2 Therefore, the original revenue results in a greater maximum monthly revenue. 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. g(x) = 6x3 + 30x2 36x Vertex form is Range: 0 f(x) 25. c. Compare the graphs. n(x) = \(\frac{3}{2}\)x2 a = 5 3. 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. Since f, h are even functions. The formula should be -b/2a 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. f(x) = x2 + x 2 Tell whether the data can be modeled by a linear, an exponential, or a quadratic function. Question 107. Label the vertex, axis of symmetry, and x-intercepts. x = 2 The 2 equations are the same line. Question 18. Range: (-, 4], Question 2. Question 77. y = bx + c. Question 31. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. 1.4 = -21a The domain of the function is all real numbers. Use the pattern to write an expression for y when x = 6.