Answer: Question 3. f(t) = -16t2 + 88t + 12 Explain. So, the x-intercepts are (-1.5, 0) and (1.5, 0) Which waterfall follows the narrowest path? y = 2(x-2)(x-2) Answer: Question 44. Answer: Answer: Reflection about the x-axis a = 4 and b = 24 g(x) = \(\frac{1}{2}\)f(x) Answer: What are the x-intercepts of the graph of y = ax2 + bx? f(x) = a(x h)2 + k Question 7. MODELING WITH MATHEMATICS Use the vertex form: The axis of symmetry is x = 2. g(-x) = af(-x) A possible answer is: a = 1, b = 2, c = 3. Given equation 3x2 12x + 12 = 0 Town A can be modeled using y = a(1 + r)t In Exercises 3538, match the function with its graph. f(x) = a(x 1)2 + 8 WHAT IF? f(x) = 2x2 + 12x + 4 y = \(\frac{1}{2}\)x 2 Question 31. g(x) = 2(x + 5)2 f(x) = -5(1)2 + 10(1) + 7 x = -b/2a = 3x2 + 2. A portion of a roller coaster track is in the shape of a parabola. Maximum value: 18, Question 19. Compare the graph to the graph of f(x) = x2. Answer: Differentiate f(x) = mx 2 HOW DO YOU SEE IT? a = -300/3600 = -1/12 Make sure your notes are visually neat for easy recall. Consider function g in Example 3. If x = 2 2(2) 3 = 1 Explain your reasoning. Use the vertex form: x = (p + q)/2 h(x) = 2f(x) Are there more?? 0 = 3600a + 300 How does the value of h affect the graph of y = a(x h)2? Question 43. x 1 = 0 or x 4 = 0 vertex: (4, 8) Given, = -(2)2 + 4(2) + 12 If x = 4 2(4) 3 = 5, Question 2. h(x) = -x2 4 = (2 + 5)/2 = 7/2 = 3.5. -16t12 + 16t1 = 0 g(x) = f (x + 5) The function g(x) = f(x) + 1 involves addition of 1 to f(x) therefore g(x) involves a 1 unit shift upward of the graph of f(x) y = 2(5/2)2 10(5/2) + 13 = 1/2 Answer: Question 54. Answer: In the function f(x) = a(x p)(x q) Answer: (-1, 2), (-2, 8), (-3, 32), (0, \(\frac{1}{2}\)), (1, \(\frac{1}{8}\)) You can find Chapterwise Algebra 1 BigIdeas Math Answer Key Organized in an efficient manner on our page. Question 3. y0 = y(2) Explain the process you used. Question 17. f(x) = -1(x +8)(x + 3)(x) Question 77. Describe the domain and range. The x-coordinate of the vertex is -0.5. MAKING AN ARGUMENT Comparing x-Intercepts with the Vertex Then write the function. Question 3. Step 2: Plot the vertex: Vertex is (h, k) = (59, 300) x = (p + q)/2 = 4 The first differences are constant at 19 so the function is linear. Function p is an exponential function and function q is a quadratic function. y = \(\frac{7}{8}\)x + \(\frac{3}{2}\) The third graph involves an exponential function. f(t) = -16(t 2.75) + 133 range: y 10 y = 36 represents 36 ft, the initial height the apple was dropped. f(x) = (x 8) + 8 Answer: Question 6. Graphing f(x) = ax2 + c, p. 426, Section 8.3 Answer: y = (0)3 4(0)2 11(0) + 30 = 30 \(\sqrt{121}\) So we replace x with r(x) with -x a. Predict how much residents will spend on pets or pet-related products and services in Year 7. y(-3) = 4(-3)2 + 24(-3) + 13 x = \(\frac{b}{2a}\) Answer: The basketball player releases another shot from the point (13, 0) and makes the shot. f(7) = f(6) + f(5) = 8 + 5 = 13 Thus maximum height is 18 feet and after achieving it the softball hits the ground. Use the zeros and the other point given to write a quadratic or cubic function represented by the table. Answer: Question 64. Width of arch = 500 (-500) d(x) = \(\frac{1}{5}\)(x 5)2 f(9) = f(8) + f(7) = 21 + 13 = 34 = -4/2(1) = -2 Plot the points (-9, 0) and (3, 0) ANALYZING RATES OF CHANGE x-intercepts: -4 and 2; range: y -3 Big Ideas Math Algebra 1 - Chapter 5: Solving Systems of Linear . Direct link to Xochitl Dachenhausen's post When I click on the algeb. Odd, Question 12. Thus the domain is [0, (4 + 32)/4] Answer: Question 8. a 1 unit downward shift, Question 4. MODELING WITH MATHEMATICS Question 43. Answer: Question 18. n(x) = \(\frac{3}{2}\)x2 = 4 Answer: n2 + 5 Answer: Question 22. Thus the function that models the given data is f(x) = (1/2)x, Question 24. The function y = -16x2 + 36 represents the height y (in feet) of an apple x seconds after falling from a tree. The first differences are: -8, -16, -24 The points appear to represent an exponential function. Answer: Question 26. Answer: The range implies that the parabola opens upward and the vertex is at (0, 3) Since f is even function, we get The vertex is at (h, k) and Question 3. y = 0.5x2 + \(\sqrt{2x}\) x 3 Free Easy Access Student Edition - Common Core High School. Since 3.6ft > 3 ft, then the ball will clear the net. y = 2x + 3/2 The function is even is it satisfies: The table shows the breathing rates y (in liters of air per minute) of a cyclist traveling at different speeds x (in miles per hour). = 4 16 + 5 Answer: Question 31. y = 5(x 3) + 2, Graph the quadratic function. Answer: Answer: f(x) = \(\frac{1}{2}\)x2 + 2x + 16 f(0) = 3(0)2 48 = -48 Identify characteristics of the quadratic function and its graph. y = x + 5 In what year were the populations about equal? 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 Question 9. So, the points (0, 3) and (-4, 3) lie on the graph. f(x) = 1(x 4) + 8 Answer: Question 84. a = 1 Answer: x = 0 Answer: = 5(4) 9 Question 6. f(x) = 5(x-(-3)) + 4 Displaying all worksheets related to - Student Jouranal Big Ideas Math Grade 7 51 Practice. = -11, Question 8. iii. = g(x) y intercept is c = 13. Answer: Question 5. a = -2, b = 8 f(x) = mx + b Let t1 be the time at which horse hits the ground. b. b. b = -2ahx Explain. Question 67. y = a(x h) + k Answer: Algebra 1. Answer: What is the maximum height of the pumpkin? Since f, h are even functions. 6x 2 = 0 Which of the following are true? web pages Answer: CRITICAL THINKING WRITING f(4) = f(3) + f(2) = 2 + 1 = 3 Identify characteristics of each parabola, if possible. MODELING WITH MATHEMATICS x = -10/-10 = 1 b. Step 3: Use the y-intercept to find two more points on the graph. Answer: x = -b/2a Step 2: (HSF-IF.A.3) Question 35. Core Concepts b. a 4 unit shift to the left 51.4 = a(1.11)20 Therefore the equation of the quadratic function whose graph is given Question 50. Since the second differences are constant, then it is quadratic. t1 = 0 or 1 Therefore the point (12, 10) must also be on the graph. y = x2 36 b. We observe that the two graphs have the same domain, range, axis of symmetry and are both parabolas. f(x) = -5(x + 7)(x 5) g(x) = -2(x 4)(x + 1) Continue this process. y = 0 = -36 + 11 Answer: Question 32. Range: [5, -), Graph the function. Note that there is a common ratio of 2 that you can multiply to get the next y-value. c. For which function does the average rate of change increase most quickly? Hence the vertex is (1/3, -1/3), Question 2. Match the function with its graph. y = x2 8x + 15 b. -2x2 4x + 3 Question 33. Solving a and b, a = 1.5, b = -0.5 Question 3. Plot the corresponding points: (-6, 0), (0, 0), (1, 0) Big ideas math. g(x) = \(\frac{3}{4}\)x2 At (1, 9): 9 = a + b x = 2 Assessments include prerequisite skills practice, chapter tests, course benchmarks, pre-course tests, and post-course tests. Parabolas have several recognizable features that characterize their shape and placement on the Cartesian plane. Answer: Question 46. Can a quadratic function with exactly one real zero be written in intercept form? When a quadratic function is in standard form, completing the square can be applied so that it can be transformed to vertex form. f(x) = 5(x 1)(x 3)(x 6) f(x) = -5x2 + 10x + 7 t2 = 4 The system is consistent. f(x) = x2 + x 2 We can see in graph that domain is set of all real numbers, R and range is (-, 32]. Answer: Graph the quadratic function. = -4(9) + 11 When does the pumpkin reach its maximum height? -14 = a(0 + 3)2 + 5 Use the point-slope formula: Use any point say (0, 1) to find the value of a Use any point say (0, 5) to find the value of a f(x) = 2x2 + 1; g(x) = f(x) + 2 f(x) = a(x h)2 + k Rewrite p(x): Explain your reasoning. 8(x + 1)(x 1) = 0 f(x) = -2x + 16x, Question 56. y = x2 8x + 15 1. How did you choose the model? Question 22. Question 1. x + 5 = 0 or x 1 = 0 Answer: f(x) = 3(x + 1)2 Answer: Question 4. x = 2 y = x2 x 12 (13-8)/3-2 = 5 The axis of symmetry is -1/3 20 a. f(x) = 6.38(1.11)x From the graph, the x-intercepts are -3, 0, 2 g(x) = -(x-2)(x-(-8)) y = -(x 6)2 5 a = 4 and b = -3 f(x) = -8x2 + 98 = 4/2(-1) y = (x + 1)(x 5)(x 4) Consider the graph of f(x) = a(x p)(x q). Question 19. Choose any 3 points: Question 29. f(x) = -3(x + 3)(x + 1) r(x) = \(\frac{1}{2}\)(x 2)2 4 Yes, starting at 13 days of vacation, the price for sea breeze is greater than blue water. x2 + 8x + 5 -1 = a 4 Answer: f(x) = -6x2 + 24x 20 Answer: WRITING Answer: Question 46. 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: Question 38. f(x) = (x 1)(x 4) Answer: Compare the graph to the graph of f(x) = x2. Use a graphing calculator to check your answer. Copy and complete the table. 4r + 12rs 12rs 36s In the function f(x) = a(x p)(x q) When a < 0 it opens down b. -4 = m(1) 2 Then find the value. The cable is about 203 feet above the water at its lower point. Tell whether the data can be modeled by a linear, an exponential, or a quadratic function. From t = 2 to t = 3: System D: We note that both graphs are parabolas and have the same range and axis of symmetry. In Exercises 1318, determine whether the function represented by the graph is even, odd, or neither. Answer: \(\frac{a-b}{3 a+b}\) In the graph, we can see that vertex is (0, 0). Answer: Question 24. The slopes are negative reciprocal so they are perpendicular. The charge increases 10% for each additional night. Question 36. f(x) = (x 6)(x 1) Vertex is (-3, 7) Answer: The function completely and the zeros are: 0, -9, -3. Answer: No, because 500 not a multiple of 45 as shown above. Question 18. Write an equation that represents g in terms of x. 0 = 16a + 4(9 a) Answer: x = 0 bx, where b is the common ratio. g(x) = f(x) + 7 Answer: Question 104. f(x) = 2x2 + 12x + 5 Explain your reasoning. Answer: -8x2 = -98 It is given that the vertex is (3, 2) A student takes a subway to a public library. Monitoring Progress 26: Monitoring Progress 27: Monitoring . Then write the function. 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. Explain your reasoning. s(x) = 18-(72)/3-1 = -27 Answer: Question 3. y = -1/9x. The main difference is that the graph of the given function opens wider than the graph of f(x) = x2, Question 16. Therefore the vertex of the parabola is at (-2, -9) 4 = -8a 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 = 1 If x = 0 0 + 5 = 5 Explain your reasoning. (-3, 5), (0, -1), (2, -5), (-4, 7), (1, -3) -1 when b = 0 x(x 1) 3(x 1) = 0 USING TOOLS b2, Question 27. h(x) = 4x2 36 Answer: Substitute \(\frac{3}{4}\) for a and 9 for b passes through (-5, 0), (4, 0), and (3, -16) f(x) = a(x +3)(x-4) Step 1: The intercepts of the parabola are p = 2 and q = -2. Answer: Question 14. Answer: A = 32 sq. f(x) = x y = a(x 0) + 3 If x = 1 \(\frac{1}{2}\)(1) 2 = -2\(\frac{1}{2}\) Mapping to Big Ideas Math Algebra I Click the image below to download the PDF Guide. Aliz CarrreEnvironmental Anthropologist. Answer: Question 32. Given, Step 1: The x-intercepts are 0 and 8. x = 5 or x = 3 Horizontally shifted 5 units to the right. = \(\frac{1}{5}\)(\(\frac{25}{2}\))2 5(\(\frac{25}{2}\)) + 27 Suppose Blue Water Resort charges $1450 for the first three nights and $105 for each additional night. R(n) = (120 4n)(80 + 5n) Answer: Answer: f(x) = x2 8x Explain. REASONING 5/4 9/5 not geometric sequence. 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 Thus the vertex is at (6, -8) passes through (7, 0) As c increases, the graph will be translated up and thus the vertex will go closer to the upper point A. x-intercepts: -7, -5, and 0 REASONING At 1990 (t = 2): 3000(1.2)2 = 4320 f(x) = a(x h)2 + k Question 25. = (0 8)/2 = -4. f(x) = a(x 0)(x 10) r(x) = \(\frac{1}{4}\)(x + 10)2 a. Explorer appearance is courtesy of National Geographic Society. = -24/2(-6) = 2 b. System E: Students in either pathway cover all the middle school content in two years, allowing them to reach Algebra 1 in eighth grade and advanced mathematics in high school. ISBN-10 -- ISBN-13 9781647270209 Material ID : 12516 The graph of an odd function is symmetric about the origin. The room expenses for two different resorts are shown. Answer: Answer: g(x) = f(x) + 2 = 9 + 5 Answer: Question 52. Answer: Answer: We can see that in the consecutive y-values, each subsequent y-value is divided by 4. Enhance your Math Proficiency by preparing from the Big Ideas Math Book Algebra 1 Solutions PDF available. a. h(t) = -16t2 + 16t The quadrants of the graphs are different and they are not equal to zero. y = 3x2 18x + 15 Answer: Question 28. f(x) = -x2 + 49 (a) rewrite the quadratic function in intercept form and Given the x-intercepts use the intercept form: a = -19/9 f(x) = 5(x 3)2 1 HOW DO YOU SEE IT? r(x) = f(x + 2) Answer: Question 62. Which aircraft hangar is taller? The x-coordinate of the vertex is -1 y = (x 2)(x + 2) f(x) = a(x (-8))(x (-2)) After how many seconds does the pinecone hit the ground? Question 3. ii. Write an equation that represents g in terms of x. In the given function q(x) = -(x + 4)2 + 7 we have Which function could include the point (-2, 3)? Thus the x-intercept of the given function is 2 and the axis of symmetry is x = 2. Question 7. What type of function represents the numbers of donations collected by Organization A? (-2, 8), (-1, 0), (0, -4), (1, -4), (2, 0), (3, 8) 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. Step 2: Answer: Explain your reasoning. Answer: Question 94. Explain. Question 41. Two intercepts are given (3, 0) and (13, 0) y = 45x. Question 45. y = x + 5 Therefore the equation that satisfies the given vertex and point is -x2 + 49 = 0 x 1x 3x + 3 = 0 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. Use the point (0, 8) to find the value of a: f(x) = x + x 2. y = -2x(x 5)(x 5) Using the graphing utility, the model is: The domain contains all possible x-values that the function can take on and thus in this case the domain is all real values R. Answer: Let the year x represent the independent variable. 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 intercepts of parabola in intercept form are given p = 0 and q = -8 Vertex is (2, -3) Axis of symmetry: x = -2 x = -b/2a f(x) = a(x h)2 + k The graph of y = ax2 + c has a vertex of (0, c) and an axis of symmetry of x = 0, Question 2. (2)x Explain your reasoning. Capture a web page as it appears now for use as a trusted citation in the future. Answer: The graph is even because it is symmetric about the y-axis. Question 7. Answer: f(x) = a(x p)(x q) Question 59. The graph of g(x) = ax will be wider than the graph of f(x) = x if 0 < |a| < 1. Answer: y = \(\frac{7}{4}\)x + 3 Answer: Question 85. 5x2 9 The shot also passes through the point (10, 1.4). 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 Open Access Materials 0 = -3(x + 3)(x + 1) The maximum height corresponds to the vertex where the x-coordinate is x = -b/2a y = \(\frac{1}{2}\)x2 6x + 10 4a + 2b = 5 If x = 2 2 + 5 = 7 The maximum height is 18 feet. Plot the corresponding points: (-9, 0), (-3, 0), (0, 0) Compare the rate of change using the average rate of change = 12 4 Enhance your conceptual knowledge by practicing the Step by Step Big Ideas Math Solutions for Algebra 1 and bridge the knowledge gap. The graph is symmetric about the y-axis. We can see in graph that domain is set of all real numbers, R and range is [-16, ), Question 16. Differentiate f(x) = a(x + 2)(x + 5) f(x) = a(x p)(x q)(x r) To explore the answers to this question and more, go to a. 1 Answer: y = (1)(x 0) + 3 Describe advantages of writing the function in each form. Answer: Question 14. 459468). Answer: x = -3 or x = 1 q(x) = |x + 6| The ball reaches its maximum height after \(\frac{7}{8}\) second when it is thrown with an initial vertical velocity of ______ feet per second. f(x) = -1/2(x + 8)(x + 2) Question 10. Essential Question What are some of the characteristics of the graph of a quadratic function of the form f(x) = ax2? Answer: Question 74. f(x) = 5x2 + 10x 3 4a = 4 Write and graph a quadratic function that models the path. For the given graph the x-intercepts are 6 and 10. The graph of f(x) = x2 is wider than the graph of g(x) = dx2 when |a | > |d| . 4 = 4a y = 3x2 2x Compare the graphs of y = 2x2 + 8x +8 and y = x2 without graphing the functions. B? The intercept form is: 9a = 3 Question 10. CRITICAL THINKING Which balloon is in the air longer? x = 7/2. f(x) = -2(x 4)2 8; g(x) = -f(x) -4 = -a(6) Substituting x = 0, the y-intercept is b. Answer: Question 8. Compare the graph to the graph of y = 4x2. x-intercepts: -2 and -5 Question 43. Direct link to joligallo7's post Are there classes like th, Posted 5 years ago. Question 27. The vertical compression by a factor 1/2 The vertex is (3, 6). p = 75 and q = 425 The y-intercept of the graph is 5. Answer: Question 26. Answer: Graph the function. Question 3. Question 63. x = -b/2a f(x) = ax2 + bx + c The given statement is sometimes true, because the graph f(x) = x2 is narrower than the graph of g(x) = x2 if a > 1, wider if a < 1 and equaly wide of a = 1. y = 9 18 + 5 where (h, k) is the vertex. This is because the three other graphs are parabolas which are graphs of quadratic functions. 0 = x f(x) = -6(x + 3)(x)(x 2) Where do I Get Chapterwise Algebra 1 BigIdeas Math Answer Key? 11. passes through (0, 0), (10, 0), and (4, 12) Answer: Question 28. Question 6. . Vertex is (2, 4). Question 13. x(x 1) = 0 Construct a table from x = 0 and x = 3 Note that there is a common ratio of 0.5 that you can multiply to get the next y-value. y increases as x increases when x < 4; y decreases as x increases when x > 4. Answer: y = -2(x 3)(x + 4) = -4(-2)(2) = 16 The graph of h(x) is a vertical shrink by a factor of 1/3 of the graph of f(x) What definition and characteristics of the graph of a quadratic function did you use to answer Exercise 44 on page 438? Answer: Question 45. The main difference is that the graph of the given function opens wider than the graph of f(x) = x2. The axis of symmetry is x = 2, so the x-coordinate of the vertex is 2. Write a quadratic function in standard form whose graph satisfies the given condition(s). Answer: c. The range implies that the parabola opens upward and the y-coordinate is -6 Your friend claims that the rotational speed of the water would have to increase for the cross section to be modeled by y = 0.1x2. 2 = a(3)2 1 Range: {y R : y 25/2}, Question 3. 4400 E. 10th Street Long Beach, CA 90804 . = -3/2(-3) = 1/2 = 0.5, Question 12. a = 1/9 Question 13. y = \(\frac{1}{8}\)(x 4)2 The function shown models the height (in feet) of a softball t seconds after it is pitched in an underhand motion. Answer: Question 50. Answer: g(x) = 2x2 + 1 + 2 He conducted meta-analyses and compared the . Which birdbath is deeper? f(x) = a(x + 5)(x + 1) given, The graph of f(x) = x2 is wider than the graph of g(x) = x2 when 0 < |a| < 1. y = -x2 + 5x a. Click the image below to download the PDF Guide. x 6 = 0 or x 1 = 0 q(x) = \(\frac{1}{2}\)x2 + 6 Thus the correct answer is option C. Question 2. Answer: Question 76. Explain how you can use your height estimate to calculate a. f(x) = 3x2 27 y = -(x + 5)(x 1) The Algebra 1, Geometry, and Algebra 2 program purposefully integrates five key strategies proven to have the highest impact on student achievement. x = 5 or x = 3, Question 36. At(4, 0): 0 = 16a + 4b The x-intercepts are -3 and -1 b. Explain your reasoning. f(x) = 2(x 1))2 + 1 Answer: Solve the equation. Answer: x = -1 and x = -7 Answer: x = 6, Question 22. 5.0 (3) $99.00. f(x) = a(x + 2)(x 1) The formula should be -b/2a f(x) = a(x p)(x q)(x r) f(x) = \(\frac{1}{3}\)(x + 5)(x 1) y = 2(x 6)2 + 1. 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 y = 2x 3 If r(-x) = r(x) function is even Answer: Question 37. Work with a partner. x = \(\frac{-b}{2a}\) The graph is a curve that is decreasing from left to right therefore it must involve an exponential function. Use the other point (5, -40) to find the value of a Use the BIM Textbook Answer Key Algebra 1 as a quick reference to clear your queries. Axis of symmetry is x = -2 In Exercises 6568, rewrite the quadratic function in vertex form. The graph of a quadratic function is shown. From the above graph, we observe that there is approximately 300 calories in a burger containing 12 grams of fat. Graph the axis of symmetry x = 3 + (-5)/2 = -1 g(-x) = f(-x) + ah(-x) (4, 51n 7), (5, 85n 19) What do you notice about the x-coordinate of the vertex of each graph? 3x = 9 or 4x = -12 (x + 4)(x + 3)(x 3) = 0 g(x) = f(x) + 1 f(x) = \(\frac{1}{15}\) (x 3)(x 13) The y-coordinate of vertex is y(0) Answer: Answer: maximum value; 10. Also, domain is all real numbers and range, as we can see from is y -1, Use zeros to graph the function. Write a function that models the data. Waterfall 1 h = -3.1d2 + 4.8 For the given graph the x-intercepts are 1 and 7. Explain. -27 = a(9)(9 10) y = 2x2 8x + 8 f(x) = \(\frac{1}{2}\)x2 2; g(x) = f(x) 6 x = 0 Answer: m(x) = \(\frac{1}{2}\)x2 4 c. Answer: How high is the road above the water? Describe the domain and range of the function. 8 = a = 4/2(1) = -2 -36 = a(-6 + 8)(-6 + 3)(-6) Question 5. At vertex (h, k) = (0, 3) Let f(x) = 3x2 1 and g(x) = f (x) + 3. What do you notice about the average rates of change when the function is increasing? f(x) = -4(x + 3)2 + 1 b. y = -x + 7 f(1) = -3(1)2 + 6(1) + 9 = 12 vertex: (-2, -4); passes through (-1, -6) we have a vertical stretch by a factor of 6 of the parent function y = x2. a. 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. Question 3. Direct link to Josue Alfaro's post where is the PDF?, Posted 5 years ago. (x + 8)(x 8) They are listed in the following fashion. Answer: y = \(\frac{1}{2}\)x \(\frac{1}{2}\) (3x 9)(4x + 12) = 0 Question 57. a = 3 y = 0 4 Answer: Question 34. = 16, Question 20. Compare the graph to the graph of f(x) = x2. 2 = 4a + 6 0 = a(3-5) + 8 Explain. y = x2 9 Label the vertex, axis of symmetry, and x-intercepts. f(x) = -3x2 + 3x 4 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: f(x) = -3x2 + 12; g(x) = f(x) 9 Given, d. The graph is a parabola so the function is Function A. It is not possible to write a quadratic function represented by the table. x = -3 or x = 3. 12 = a(3 1)2 + 8 Question 11. h(x) = (x2 36)(x 11) Some of the questions are badly worded and you have to guess what they want to ask. With c = 10, the y-intercept is 10 therefore the parabola passes through the point (0, 10). Show your work. + 6 0 = a ( x ) = a ( x + 5 = Explain. Where b is the PDF?, Posted 5 years ago ) + k Answer: Answer: 6! Second differences are constant, Then the ball will clear the net Which function does the average of. Slopes are negative reciprocal so they are listed in the following are true follows the path. 9 the shot also passes through the point ( 10, 1.4.... The characteristics of the form f ( t ) = 2 2 ( x ) = x2 an that. 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