notice that r(-x) is equal to r(x) so function r(x) is odd function. f(x) = \(\frac{1}{2}\)(2)2 + 2(2) + 16 = 18 f(x) = a(x 0)(x 10) 9/9/15 2:20 PM. 16t2 = 25 Which waterfall drops water from the highest point? f(x) = -6(x + 3)(x)(x 2) a(-4 + 5)(-4 + 1) = 3 x-intercepts: -2 and -5 Answer: Graph the function above and graph y = x2 b. Waterfall 2 h = -3.5d2 + 1.9 x + 6 = 0 or x 6 = 0 or x 11 = 0 t1 = 1s. a. Answer: Answer: Answer: Question 5. f(x) = x2 + x 2 b. Answer: Answer: The 2 equations are the same line. Given, 20 Explain your reasoning. = -4.25 Describe and correct the error in graphing the function f(x) = -x2+ 4x + 3. Answer: Question 24. a = 1 Answer: 0 = x Answer: t(7) t(2)/7 2 = 29.55 The vertex form of the quadratic function is Hence the vertex is (-3, -4), Question 3. x = 0 or x = 1, Question 82. h(t) = = -16t2 + 32t + 2 This class does not use problems from the textbook, and does not teach the concepts using the same methodologies as the textbook. y = -2x3 + 20x2 50x y = -(3)(-3) MODELING WITH MATHEMATICS The vertex is (-1, 1). Answer: Question 68. x0 = -b/2a Question 23. a. Classify each function as linear, exponential, or quadratic. We are given that (119, 0) lies on the graph. Since the second difference is constant, then the function is quadratic. Answer: When I click on the algebra 1 book, it only takes me to chapter 7. Satellite dishes are shaped like parabolas to optimally receive signals. What tends to happen to the number of calories as the number of grams of fat increases? b. Click on the Topic-wise Big Ideas Math Algebra 1 Solutions of Chapter 8 and clear all your queries regarding the concepts. 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. \(\frac{7}{3}\). Answer: Question 44. y = 32. = (x 1)2 + 6 How does the value of h affect the graph of y = a(x h)2? g(x) = 6x3 + 30x2 36x f(x) = \(\frac{1}{9}\)(x 30)2 + 25 h(x) = x2 + 8 The function 3y = 2x 14 represents the height of the bleachers. f(-0.5) = -2(-0.5 3)(-0.5 + 4) = 24.5 Answer: Question 54. f(x) = 5(-1)2 + 10(-1) 3 a. Question 69. Answer: Answer: f(x) = 5x2 + 10x 3 441448). Question 13. Answer: b. Graphing y = a(x h)2 When h < 0 Chapter 5: Solving Systems of Linear Equations, Chapter 6: Exponential Functions and Sequences, Chapter 7: Polynomial Equations and Factoring, Chapter 10: Radical Functions and Equations, Chapter 3: Parallel and Perpendicular Lines, Chapter 6: Relationships Within Triangles, Chapter 7: Quadrilaterals and Other Polygons, Chapter 9: Right Triangles and Trigonometry, Chapter 11: Circumference, Area, and Volume, Chapter 3: Quadratic Equations and Complex Numbers, Chapter 5: Rational Exponents and Radical Functions, Chapter 6: Exponential and Logarithmic Functions, Chapter 9: Trigonometric Ratios and Functions. Question 33. Answer: Answer: Using the vertex form, the graph of f(x) is the graph of g(x) is: The slopes are negative reciprocal so they are perpendicular. b. Answer: Will the ball clear the net? Let g(x) = f(x) + ah(x) Question 11. g(x) = f (x + 5) Thus the function that models the given data is f(x) = 5 . y0 = h(1/2) Answer: y = 2x2 + 8x + 3 f(x) = -5x2 + 10x + 7 The vertex is (6, 9). Answer: Question 40. Answer: Range: y 8 a 1 unit downward shift, Question 4. 2. Chapter 1 Solving Linear Equations Chapter 2 Solving Linear Inequalities Chapter 3 Graphing Linear Functions Chapter 4 Writing Linear Functions Answer: y = 2(x + 1)2 3 0 = a(3-5) + 8 Since the vertex is located at the axis of symmetry, we can find the y-coordinate by substituting x = 2 You can find Chapterwise Big Ideas Math Answer Key for Algebra 1 with step by step explanation on this page. Step 3: COMPLETE THE SENTENCE Work with a partner. Question 11. Compare the graph to the graph of y = 4x2. Step 3: A = 32 sq. Answer: -2 = a 0 = 16a + 4(9 a) The width is the distance between the 2 x-intercepts a. Work with a partner. Vertex: (6, 0) y = x2 8x + 15 The y-coordinate of vertex is y(-3) vertex: (1, 8); passes through (3, 12) x = (p + q)/2 g(x) = 5x2 Let g(x) = af(x) Write the function represented by the graph in intercept form. a = 1 Explain. If x = 3 2(3) 3 = 3 f(x) = 3x2 + 4 If x = 0 \(\frac{1}{2}\)(0) 2 = -2 y = \(\frac{1}{2}\)x2 6x + 10 MODELING WITH MATHEMATICS c. A manila rope has four times the breaking strength of another manila rope. Does the graph open up or down? Thus the function is odd, Question 2. y = x2 2x + 7 5 = a(6 1)(6 7) -2r(-2r 6s) + 6s(-2r 6s) Next. = 8, Question 7. Answer: Label the vertex, axis of symmetry, and x-intercepts. Find the height and width of the arch. Compare the graph to the graph of f(x) = x2. To find a, substitute either (-6, -4) or (6, -4) b. y = (x + 3)2 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 1 unit. = -g(x) Answer: Question 20. 0 = -16t2 + 25 y = \(\frac{1}{2}\)x2 11x + 6 a = 4 and b = -3 https://play.google.com/store/apps/details?id. x = 8/2(8) = 1/2 = 0.5 Axis of symmetry is f(x) = -5x2 + 20x 7 Step 1: The intercepts of the parabola are p = 2 and q = -2. Substitute the intercepts and simplify: Evaluate the expression. g(x) = -2(x 4)(x + 1) The basketball player releases another shot from the point (13, 0) and makes the shot. Which of the following are true? We note that both graphs are parabolas and have the same range and axis of symmetry. The axis of symmetry is 2 Find the average rates of change of each function for each 1-hour interval from t = 0 to t = 6. f(x) = (x 6)(x 1) y = 2(x+2)(x + 2) f(x) = a . -2 = a(1) x2 + 8x + 5 (x + 8)(x 8) y = 6x 2 The zeros also the x-intercepts: 3, 7 The area A (in square feet) of a square patio is represented by A = x2, where x is the length of one side of the patio. The x-coordinate of the vertex is 4 HOW DO YOU SEE IT? Answer: Answer: The height of the football is represented by g(x) = f (x + 5). f(x) = a(x p)(x q)(x r) x = -2 USING STRUCTURE In Exercises 8790, match the function with its graph. Plot the points (3, 0) and (-5, 0) Equation must have a vertex at (1, 2). For this equation to be true, we can let b = 0 so that a and c any value. Question 7. WRITING Answer: Question 78. where a = 3000, r = 0.2 d. Compare the value of the x-coordinate of the vertex with the values of the x-intercepts. Direct link to joligallo7's post Are there classes like th, Posted 5 years ago. Also, you can attempt the Chapter 8 Graphing Quadratic Functions Assessments easily by solving all exercise questions covered in the Big Math Ideas Algebra 1 Textbook Answers. When a quadratic function is in standard form, completing the square can be applied so that it can be transformed to vertex form. Find and interpret the x- and y-intercepts. As a Big Ideas Math user, you have Easy Access to your Student Edition when you're away from the classroom. Width of arch = 500 (-500) -4 = m(1) 2 f(x) = a(x 1)(x 7) Hence the vertex is (7, -14.5), Graph the function. 6 = a(0 + 1)(0 1)(0 2) b(x) = 2.5x2 The minimum value is attained at the vertex of parabola. = 3x2 + 2. n = -b/2a This corresponds to Graph A. j(x) = -4(x+1)(x-1). t t1 = m(t t1) b. Answer: Question 8. In Exercises 6168, use zeros to graph the function. passes through (0, 0) and (6, 0) Answer: Graph the function. R(n) = (120 6n)(80 + 8n) Answer: Apps take a long time to design and program. Answer: Question 52. 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. Answer: Question 3. Which polynomial represents the area (in square feet) of the shaded region of the figure? y = \(\frac{3}{4}\) x2 + 9x 18 f(x) = 5x axis of symmetry: x = -5 c. Describe where the function is increasing and decreasing. This corresponds to Graph B. Compare the graph to the graph of f(x) = x2. Describe and correct the error in graphing and comparing y = x2 and y = 0.5x2. x = -b/2a = -2(4) + 8 + 3 b. b. (x 1)(x 4) = 0 Question 33. y = 2(x 6)2 + 1. notice that w(-x) is not equal to -w(x) = -5x or w(x) The PDF gives you a preview of videos and exercises to save you time in identifying relevant resources. Given, Previous Answer: Question 31. x2 2x + 1 + 6 y0 = f(\(\frac{25}{2}\)) Question 45. Given, g(x) = 3x2 12x + 12 y = -(-2)2 4(-2) + 2 y = -2x2 + 6x + 8 Which car is accelerating the most? (a) rewrite the quadratic function in intercept form and Compare the rate of change using the average rate of change a = -2 and b = 8 Function p is an exponential function and function q is a quadratic function. Given, Algebra 1. Step 2: VOCABULARY 2. a. If so, by how much? MODELING WITH MATHEMATICS Question 3. Domain is (-, +) 16t2 = 64 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. Find the y-value of the vertex by substituting 5 to x Core Concepts Explain your reasoning. The y-intercept is 3. Explain. Answer: p = -3 and q = 4 x = 90 meters. The opening of one aircraft hangar is a parabolic arch that can be modeled by the equation y = -0.006x2+ 1.5x, where x and y are measured in feet. Answer: Question 3. q(x) = x2 1 Describe why your answer makes sense considering the context of the data in Exercise 20 on page 466. Answer: Use zeros to graph the function. The third graph involves an exponential function. x(x 1) = 0 Some of the questions are badly worded and you have to guess what they want to ask. MODELING WITH MATHEMATICS y = -3x2 + 6x + 9 Given function Area of trapezoid = \(\frac{1}{2}\)(b1 + b2)h 3, 11, 21, 33, 47, . Answer: = -25. Answer: b. \(\sqrt [ 3 ]{ 125 }\) Therefore the vertex of the parabola is at (-2, -9) Use a graphing calculator to verify your answers. Answer: f(x) = x (x + 5)(x 3) = 0 Label the vertex, axis of symmetry, and x-intercepts. f(x) = a(x 59)2 + 300 a = 1/9 y intercept is c = 13. ERROR ANALYSIS The axis of symmetry is x = -2 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. Be the first one to, Big ideas math. The graph of f(x) = x2 is narrower than the graph of g(x) = x2 when a > 0. The vertical compression by a factor 1/2 Answer: x = 24/2(4) = -3 g(x) = (x 1)(x 3)(x + 3) Since the height corresponds to the location of the vertex, we can use it as an additional point to find the value of a. ANALYZING EQUATIONS In Exercises 93 and 94, Question 19. 6 = 2a 2015 Big Ideas Learning, LLC. b. reflection about the x-axis of the parent function y = x, Question 8. Answer: Just click on the chapter you wish to prepare and start your preparation. The instructional design guides students through concepts from surface-level to deep-level learning and allows them to transfer these skills for success in higher-level math courses. Question 18. 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 c. Compare the graph of f to the graph of g(x) = x2. x2 + 8x + 5 -2 = a . Answer: WRITING EQUATIONS What do you notice about the average rates of change when the function is increasing? 8(x2 1) = 0 g(x) = 3x2 12x + 12 Answer: f(x) = -2(x 4)2 8; g(x) = -f(x) Show your work. c = 0 Question 3. Answer: Question 28. h(x) = 3x 6 Direct link to Joscelyn Chilet's post How can I participate in , Posted 7 months ago. MODELING WITH MATHEMATICS Question 32. g(x) = 2(x)(x 2) a(-x) + b(-x) + c = -(ax2 + bx + c) Axis of symmetry: x = -1 Using technology, find a function that models the data. Question 5. Big Ideas Math Answers Algebra 1 ensures your childs success and also keeps them on the right track. Use any 2 points, g(x) = f(x) 4 Question 45. g(x) = f(x) + 2 If we write a graph in the form y = x2 2x + 7 Given, f(x) = x 16x + 72. x = -1.5 does not make sense in the context of the problem The textbook market has been cornered by a few big . Which birdbath is wider? Compare the websites in Example 4 by calculating and interpreting the average rates of change from Day 0 to Day 10. 2x B? 2x + 6 = 0 y = -(x + 5)(x 1) . b. Question 8. passes through (7, 0) Organization A begins with one donation, and the number of donations quadruples each hour. After how many seconds does the pinecone hit the ground? One way to approximate the area is by redrawing the parabola into a graph with grids then count the number of squares. y = (0)2 0 12 = -12 How does the value of c affect the graph of f(x) = ax2 + c? Explain how you found the x-intercepts. Thus is equivalent to the function f(x) = 2 . The distance traveled in t minutes is y miles. The minimum value is -4.25. The y-coordinate is Answer: Question 26. Answer: Chapter 1: Solving Linear Equations Page 1: Try It Yourself Section 1.1: Solving Simple Equations Section 1.2: Solving Multi-Step Equations Section 1.3: Solving Equations with Variables on Both Sides Section 1.4: Rewriting Equations and Formulas Page 33: Chapter Review Exercises Page 36: Chapter Test Page 37: Standards Assessment Exercise 1 f(x) = 5(x 3)2 1 To log in and use all the features of Khan Academy, please enable JavaScript in your browser. The cross section of a satellite dish can be modeled by the function shown, where x and y are measured in feet. Given, ii. y = 8(0)2 8 = -8 g(x) = \(\frac{1}{2}\)x2 2- 6 = \(\frac{1}{2}\)x2 8, Question 12. Question 75. Big Ideas MATH: A Common Core Curriculum for Middle School and High School Mathematics Written by Ron Larson and Laurie Boswell. Does the graph represent a linear or nonlinear function? x + 1 = 0 or x 1 = 0 Compare the graph to the graph of f(x) = x2. f(x) = -6x2 + 24x 20 is even and has a range of y 3 Answer: x = -6 or 6 or 11, Question 30. f(x) = a(x p)(x q)(x r) (-3)2 + 12(-3) + 5 = -13 g(x) = f(x) + h(x) This equation belongs to Graph A because it is the only graph with a vertex of (1, 3) and a reflection over the x-axis. Axis of symmetry: x = -4 Question 83. = \(\frac{1}{5}\)(\(\frac{25}{2}\))2 5(\(\frac{25}{2}\)) + 27 The vertex is at (7, 10580) x = (-5+1)/2 = -2 Compare the graph to the graph of f(x) = x2. Describe the domain and range. n2 + 5 A water balloon is dropped from a height of 144 feet. 8 = a y = 2(-2)2 + 8(-2) + 3 Question 43. f(x) = x + 12x + 35x. d 19 = 19t 19 Answer: Question 18. Answer: x = 2 + (-2)/2 = 0 f(x) = 3(x 3)2 + 6 y = 3x2 48 x2 4x + 4 = 0, Question 6. For a quadratic function f, what does f(-\(\frac{b}{2a}\)) represent? Step 4: Draw a smooth curve through the points. station58.cebu k(x) = x2 8x + 7 Answer: notice that h(-x) is not equal to -h(x) or h(x) Vertex: (3, 6) Thus the vertex is at (6, -8) 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. (8-5)/2-1 = 3 4a = -8 How does graphing a function in Exercise 27 on page 429 help you answer the questions? y = -3x + 4 (-3, 8), (-2, 4), (-1, 2), (0, 1), (1, 0.5) f(x) = a(x p)(x q) Graph the axis of symmetry x = -9 + 3/2 = -3 f(x) = 2(x 1))2 + 1 5 4 9 5 not an arithmetic sequence Answer: Using Your Book . In given function g(x) = \(\frac{1}{2}\)(x + 1)2 + 1 How can factoring help you compare the parabolas? Waterfall 1 h = -3.1d2 + 4.8 Answer: Answer: Answer: Question 24. Answer: Question 32. Thus the correct answer is option C. Question 2. Therefore the vertex of the parabola is at (0, -4), Tell whether the table of values represents a linear, an exponential, or a quadratic function. Does changing the value of p change the y-intercept? y = ax2 + c = -4(9) + 11 Therefore the vertex of the parabola is at (1, 12) x = \(\frac{-b}{2a}\) Describe the transformation from the graph of f(x) = ax2 to the graph of g(x) = a(x h)2 + k. c. The graph is an exponential growth so b > 0 which is Function B. Answer: Question 106. x = (7 + 3)/2 = 5 1.4 = a(10 3)(10 13) Does changing the sign of a change the x-intercepts? The function shown models the height (in feet) of a softball t seconds after it is pitched in an underhand motion. 459468). 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. The shot also passes through the point (10, 1.4). 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 0.5 The graph of f(x) = x2 is wider than the graph of g(x) = dx2 when |a | > |d| . h(t1) = 0 a = -1/2 f(x) = -8x2 + 98 Question 3. The parabola opens downward with the following characteristics Question 11. Each function gives the height h (in feet) and the horizontal distance d (in feet) of the water. He conducted meta-analyses and compared the . OPEN-ENDED Your friend claims that it is possible to draw a parabola through any two points with different x-coordinates. Answer: Question 28. Step 3: y y1 = m(x x1) Answer: f(x) = \(\frac{1}{5}\)x2 5x + 27 g(x) = 2x2 + 1 + 2 In the given function g(x) = x2 + 5 we have a vertical shift of 5 units upward of the parent function y = x, Question 7. x = -3 or x = 3. The second differences are: -8, -8 Then write a function that models the data. a = -1 + 4 Answer: Question 4. If x = 2 \(\frac{1}{2}\)(2) 2 = -3 All the Big Ideas Math Solutions are given by subject experts adhering to the Common Core 2019 Curriculum. y = x2 x 12 Question 6. There are 2 real zeros when the graph crosses the x-axis. = -12/2(5) = -3 2 = 4a + 6 Write a function that models the data. Answer: Question 14. Graph of 2.5x2 is narrower than x2 since it is stretched vertically by factor 2.5. ANALYZING RELATIONSHIPS Question 35. h(x) = \(\frac{1}{4}\)x2 + 4 (x2 36)(x 11) = 0 your vertex is 0.5, 4 x = -3 or x = 1 Question 87. Answer: Answer: Question 8. passes through (-5, 0), (-1, 0), and (-4, 3) y = -16x2 + 36 y = 45x. Graph the quadratic function. a = -3 Answer: Big Ideas Math Answers Algebra 1 ensures your child's success and also keeps them on the right track. y = -4+8+2 Answer: Question 62. No, Sea Breezes prices will always be greater than blue water for all number of vacations. 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. Write a quadratic function in standard form that models the path of the shot. The given is a cubic function. This equation belongs to Graph B because it is the only graph with a vertex of (-1, -3) and a vertical stretch by a factor of 2. Answer: Graph the function. Answer: Question 3. Answer: Question 34. The trajectory of the pumpkin will be a parabola, so the time required for the pumpkin to reach maximum speed is actually the x-coordinate of the vertex of the parabola and the maximum height is the y-coordinate of the vertex. To help determine the shape of the graph, find the points between the zeros and plot them. Answer: Therefore the vertex of the parabola is at (-1/2, 8) x = 1/3 Use any point say (0, 1) to find the value of a All Rights Reserved. Question 13. To help determine the shape of the graph, find the points between the zeros and plot them. -x2 + 49 = 0 So, the function w(x) is neither odd nor even. We observe that the two graphs have the same domain, range, axis of symmetry and are both parabolas. m(-x) = 2x2 + 7x Explain. x = 0 = 9 + 5 y = (x 4)(x + 2) MODELING WITH MATHEMATICS Write a quadratic equation whose graph models the shape that appears. Question 1. = -24 + 48 20 Answer: Question 30. Answer: Write the equation using the form f(x) = a . g(x) = f(x) 6 f(x) = a(x p)(x q) A kicker punts a football. x2 = 36/16 Answer: In Exercises 3538, match the function with its graph. h(-x) = 2(-x)2 + 3 Describe the domain of the function. Explain. Given, Answer: m(x) = 2x2 7x Question 29. One falls 45 feet, while the other falls 32 feet. x from -5.5 to 6.5. y = a(x p)(x q) The arch can be represented by a function of the form f(x) = a(x p)(x q). Question 22. y = 1.5x 0.5x. Therefore, the numbers that are in between 0 and 100 are: 1, 2, 3, 5, 8, 13, 21, 34, 55 and 89. Is the graph of a set of points enough to determine whether the points represent a linear, an exponential, or a quadratic function? Question 97. -72 = -12a Given, Answer: Question 48. f(x) = -(x + 1))2 2 Explain. ax2 bx + c = -ax2 bx c Answer: In the given function g(x) = -3(x + 2)2 4we have b. f(x) = a(x p)(x q)(x r) Step 1: The x-intercepts are -9 and 3. Common Core Assessment Practice for Mathematics. y = \(\frac{1}{2}\)(x 1)2 + 3 f(t) = -16t + 80t + 5 Refer to the Algebra 1 Big Ideas Math Answer Key and clarify all your concerns. Question 6. You can find Chapterwise Algebra 1 BigIdeas Math Answer Key Organized in an efficient manner on our page. a. y = (x 3)2 y = 3000(1.2)t Compare the graphs of y = 2x2 + 8x +8 and y = x2 without graphing the functions. y -2x2 + 20x 42 Make sure your notes are visually neat for easy recall. x = -1 Can a function be symmetric about the x-axis? Answer: Question 32. a. a vertical stretch by a factor of 2 = 3, Question 10. Function is even if f(-x) = f(x) and function is odd if f(-x) = -f(x) g(x) = f(x) 3 Question 10. When a > 0 it opens up, Monitoring Progress and Modeling with Mathematics. r(x) = -6x2 + 5 In Exercises 5760, write the quadratic function represented by the graph. f(x) = -x(x + 9)(x + 3) So, the vertex is (-1, 32) g(-x) = -f(x) + a(-h(x)) = -g(x) 3x 9 = 0 or 4x + 12 = 0 f(x) = a(x + 2)(x 1) Given, y = -3x + 5 Answer: Question 52. Compare the graph to the graph of f(x) = x2. Axis of symmetry: x = 6. We note that both graphs are parabolas and have the same range and axis of symmetry. 0 < a < 1 4r 36s. x = (p + q)/2 = 4 f(x) = 2(x 1))2 + 1 Work with a partner. f(t) = -16t2 + 88t + 12 How can you use technology to confirm your answer in Exercise 64 on page 448? \(\frac{a-b}{3 a+b}\) Step 1: Find axis of symmetry: Answer: Answer: f(x) = 3x2 2x Range: 0 f(x) 25. c. Compare the graphs. Question 1. f(10) = f(9) + f(8) = 34 + 21 = 55 The graph shows that the functions y-intercept is -2. f(x) = 5(x-(-3)) + 4 f(x) = (x 6)(x 1) Answer: When is each function decreasing? Explain. The error was in solving the equation x2 9 = 0 in a wrong way. Answer: Answer: y = \(\frac{2}{3}\)x2 6x + 5 Which bird starts its dive from a greater height? x = 3/2 = 1.5 Answer: Question 32. b. f(x) = (x 2) + 1 (4y + 2)(4y 2) Answer: Answer: Thus, parabola is of the form f(x) =ax2 WHICH ONE DOESNT BELONG? y = \(\frac{1}{2}\)(x 1)2 + 3 Then write the function. If not, explain why. -4x2 8x 4 = 0 y = -2x2 4x + 30 Solve 0 = ax2 + bx for x by factoring. Vertex: (-1, -7) (3x 9)(4x + 12) = 0 Write the given function in intercept form to have: = 2 a. Answer: Let x represent the number of decades since 1970. Answer: x-intercept:(-1, 0) and (4, 0) Use a graphing calculator to verify your answers to Question 3. Since x = \(\frac{b}{2a}\) represents the x-coordinate of the vertex, the f(-\(\frac{b}{2a}\)) is the y-coodinate of the vertex. f(x) = 1(x + 2)(x 1) 425430), Graph the function. Click on the Topic-wise Big Ideas Math Algebra 1 Solutions of Chapter 8 and clear all your queries regarding the concepts. The points (-3, 12) and (-1, 4) are the same horizontal distance from the axis of symmetry, so for both of them to lie on the parabola, they would have the same y-coordinate. y = -(x + 5)(x 1) Vertex: (-2, 6) Answer: Question 46. So, the vertex is (0, -4) y = 9 18 + 5 f(x) = -2x 2. Answer: Answer: Question 42. Therefore the point (12, 10) must also be on the graph. Graphing y = ax2 + c Answer: y0 = y(2) After how many seconds does the water balloon hit the ground? = 2x2 + 3 Complete the table. Answer: m = (d2-d1)/(t2-t1) = (38-19)/2-1 = 19 Essential Question What are some of the characteristics of the graph of a quadratic function of the form f(x) = ax2? -2 = -4a Let the time t represent the independent variable. Another birds dive is represented by r(t) = 2h(t). f(x) = 3x2 2x Range: {y R : y 25/2}, Question 3. Axis of symmetry: x = 3. A possible answer is a = 1, b = 0, c = 2 4a = 4 r(x) = 40-0/3-1 = 40/2 = 20 f(x) = -3(x + 5)2 6; g(x) = 2f(x) Reflected in the x-axis In Exercises 36, find the x-intercepts and axis of symmetry of the graph of the function. Answer: Graph the axis of symmetry x = 0 + 8/2 = 4 The cable is about 203 feet above the water at its lower point. Find the product. Big Ideas Math Answers main intention is to provide good quality of education and make students move on the right path. f(3) = f(2) + f(1) = 1 + 1 = 2 Substitute \(\frac{3}{4}\) for a and 9 for b (-3, 5), (0, -1), (2, -5), (-4, 7), (1, -3) 2. What is the maximum height of the pumpkin? f(x) = (x 8) + 8 Question 2. Consider the graph of f(x) = a(x p)(x q). y = 0.00016(1888)2 0.46(1888) + 507 = 203 3x2 + x 2 Question 3. Answer: b. = 1/2 The axis of symmetry is at x = -b/2a Answer: In Exercises 3136, match the function with its graph. The first differences are: -12, -12, -12 In the function f(x) = a(x p)(x q) Answer: Then describe its graph. x 6x -x + 6 = 0 The pinecone hits the ground at y = 0 The graph is a line so the function is: Function D The arch support of a bridge can be modeled by y = -0.0012x2, where x and y are measured in feet. -4 ) y = 0.00016 ( 1888 ) 2 + 300 a = -1 + Answer. Corresponds to graph a. j ( x ) = x2 and y are measured in feet ) of graph! Just click on the right track domain, range, axis of symmetry: x = -4 ( )!, and the number of squares 3 b. b 2.5x2 is narrower than x2 it... The y-intercept 3 Describe the domain of the parent function y = x, Question 4 -4... 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