31. WRITING Two quadratic functions have graphs with |32. WRITING A quadratic function is increasing to the left vertices (2, 4) and (2, -3). Explain why you can not of * = 2 and decreasing to the right of x = 2. Will the use the axes of symmetry to distinguish between the vertex be the highest or lowest point on the graph of two functions. the parabola? Explain. In exercise 36 37. ANALYZING EQUATIONS The graph of which x is the horizontal function has the same axis of symmetry as the graph distance (in feet) of y = x + 2x + 2? and y is the vertical 35 (A) y = 2r + 2r + 2 EXPLAIN: distance (in feet). The path of a shot put released at an angle of 35% (By= -3 - 6x + 2 can be modeled by y = -0.01x] + 0.7x + 6. Find and Oy=x-2+2 interpret the coordinates of the vertex. (D) y= -5r + 10r + 2 38. USING STRUCTURE Which function represents the widest parabola? Explain your reasoning. (A) y = 2(x + 3) EXPLAIN: By=x-5 Ox-054x- 1)+ 1 Dy=-x+6 In exercises 39-48, find the minimum or maximum value of the function. Describe the domain and range of the function, and where the function is increasing and decreasing. 39. y = 6r- - 1 42. g(x) = -3x - 6r + 5 45. h(x) = 2x2 - 12x 48. Ax) = x + 6x + 4 49. PROBLEM SOLVING The path of a diver is modeled 66. MODELING WITH MATHEMATICS Although a football by the function f(x) = -Qx- + 9x + 1, where f(x) is field appears to be flat, some are actually shaped the height of the diver (in meters) above the water and like a parabola so that rain runs off to both sides. x is the horizontal distance (in meters) from the end of The cross section of a field can be modeled by the diving board. y = -0.000234x(x - 160), where I and y are a. What is the height of the diving board? measured in feet. What is the width of the field? What is the maximum height of the surface of the field? b. What is the maximum height of the diver? surface of football field c. Describe where the diver is ascending and where Wat drawn to kal the diver is descendingGraph the function. Label the x-intercept(s), vertex, and axis of symmetry. 56. Ax) = 2(x - 5)(x - 1) 57. g(x) = -x(x + 6) x-ints: X-ints: vertex: vertex: axis of sym: axis of sym: 73. PROBLEM SOLVING A woodland jumping 74. HOW DO YOU SEE IT? Consider the graph of the mouse hops along a parabolic path given by function /(x) = aux - plus - q). y = -0.2r + 1.3r, where x is the mouse's horizontal distance traveled (in feet) and y is the corresponding a. What does/ 2 - ") represent in the graph? height (in feet). Can the mouse jump over a fence that is 3 feet high? Justify your answer. b. If a Cale, #5 Quad Reg Graph? Scroll to "Store RegEQ". Press ALPHA F4 . Press enter 3 times! 2ND STAT PLOT Plot 1 ON; ZOOM #q Name: Hour: A2 02.08 Modeling with Quadratics Day 2 Textbook Page 92: 4, 6, 8, 10, 12, 14, 16, 18, 19, 21, 24-27 In exercises 4-8, write an equation of the 6. passes through (-7, -15) and has a vertex of (-5, 9). parabola in vertex form. 18. 37 8. passes through (6, 35) and has a vertex of (-1, 14). In exercises 4-8, write an equation of the 12. x-intercepts of 9 and 1; passes through (0, -18) parabola in Intercept form. 10. 1-27 (2, 0) -1, 0) 14. x-intercepts of -7 and -3; passes through (-2, 0.05) Unit Two Page 816. Which of the following equations Write an equation of the parabola in vertex form or intercept represent the parabola? form for questions 18 and 19. 19. Human Jump 18 New Ride 1-21 160 (1 164) (3, 2.25) Height (feet) Height (feet] 2 (0.5. Distance (feet) (A y = 2(x - 2kr + 1) Time (seconds] By = 2(x + 05) -4.5 O y- 2(x - 0.5) - 4.5 "D) y = 2(x + 2Xx - D) EXPLAIN: 24. MODELING WITH MATHEMATICS A baseball is thrown up in the air. The table shows the heights Time, x 0 2 4 " (in feet) of the baseball after x seconds. Write an Baseball height. y 6 22 22 6 equation for the path of the baseball. Find the heigh of the baseball after 5 seconds. 25. COMPARING METHODS You use a system with three 26. MODELING WITH MATHEMATICS The table shows the variables to find the equation of a parabola that passes distances y a motorcyclist is from home after & hours. through the points (-8. 0). (2, -20), and (1, 0). Your Time (hours), x 2 3 friend uses intercept form to find the equation. Whose Distance (miles). y 45 90 135 method is easier? Justify your answer. Write and evaluate a function to determine the distance the motorcyclist is from home after 6 hours. -27. USING TOOLS The table shows the heights b. Use the regression feature of your calculator to h (in feet) of a sponge / seconds after it was dropped find the model that best fits the data. by a window cleaner on top of a skyscraper. Time, t 0 1.5 25 3 c. Use the model in part (b) to predict when the Height, h 280 264 244 180 136 sponge will hit the ground. a. Use a graphing calculator to create a scatter plot. Which better represents the data, a line or a parabola? Explain. d. Identify and interpret the domain and range in this situation.A2 02.09 Discrete: Continuous: Discrete and Continuous Data 1.) The function y = 1.5x represents the [x. V) cost y (in dollars) of renting x DVDs at a store. Each customer can rent a maximum of 5 DVDs. 15 (1. 15) a.) Is the domain discrete or continuous? 2 3 (2. 3) Explain. 45 03.49 4 (4. 6) b.) Graph the function using its domain. 75 (5. 7.5) 2.) The function y = -16x7 + 48x + 3 represents the height (in feet) of a volleyball x seconds after it is hit into the air. a.) Is the domain discrete or continuous? Explain. b.) Graph the function using its domain. Identify each situation as discrete or continuous. Explain why. 1. The function m = $5 - 10.5x represents the amount mi (in dollars) of money you have after purchasing & t-shirts. 2. The function c = 2.25x represents the cost c of purchasing p pounds of blueberries at a fruit stand. 3. A kicker punts a football. The height h (in yards) of the football is represented by h = - -(x - 30) + 25, where x is the horizontal distance Name: Hour: A2 02.09 Discrete and Continuous Data 1.) The function m = 15.5x represents the amount m |2.) You purchased a lawnmower for your after- (in dollars) of money you have after selling x tickets. school business. The function p = 15x - 75 You have six tickets to sell. represents the amount p (in dollars) of profit you *: count by 1; y count by 10 | have after mowing the yards of x customers. *: count by 1; y count by 10 a. Is the domain of the a. Is the domain of the function discrete or function discrete or continuous? Explain. continuous? Explain. b. Graph the function b. Graph the function using using its domain. its domain. Unit Two Page 103.) The function represents the amount g (in gallons) |4.) An outfielder throws the softball. The following of gasoline you have in the tank after driving x miles. function represents the height (in feet) of the softball 1 g = 20 - x: count by 25; y count by 2 x seconds after it is thrown into the air. h = (x - 5) + 30 * count by 1; y count by 5 a. Is the domain of the function discrete or a. Is the domain of the continuous? Explain. function discrete or continuous? Explain. b. Graph using its domain. b. Graph using its domain. 5.) The function g = 100 - 20x represents the 6.) A bird swoops down for its prey and then flies up number g of glasses left to be boxed after shipping into the sky. The height h (in feet) of the bird is glasses in x boxes. x: count by 1; y count by 10 represented by the following equation, where x is the a. Is the domain of the horizontal distance (in feet) from the original perch. function discrete or * count by 1; y count by 2 continuous? Explain. h = -(x - 5) +8 a. Is the domain of the function discrete or b. Graph using its domain. continuous? Explain. b. Graph using its domain. Name: Hour: A2 02R Review of Unit 2 Describe the transformation of f(x) = x' represented by g. 1. 2. a.) a.) b. ) b. ) b.1 Write a rule for g and identify the vertex. 4. Let g be a translation 2 units up, followed by 5. Let g be a horizontal shrink by a factor of -, a reflection in the x-axis and a vertical stretch by a factor of 4 of the graph of f(x) = x. followed by a translation 2 units up and 4 units left of the graph f(x) = (3x - 2) + 5. Rule: Rule: Vertex: Vertex: Unit Two Page 11Graph the function. Label the vertex and axis of symmetry. 6. /(x) = 3(x - 4) + 2 7. f(x) = 5x' + 4x- 1 Vertex: Vertex: Axis of Symmetry: Axis of Symmetry. Find the x-intercepts of the graph of the function. Then describe where the function is increasing and decreasing. 8. g(x) = -1(x - 4)(x + 2) 9. g(x) = 1(x - 6)(x - 3) x-intercepts: x-intercepts: Describe where function is increasing and Describe where function is increasing and decreasing: decreasing: 10. An object is launched directly overhead at 36 meters per second. The height (in meters) of the object is given by h(t) = -161 + 361 + 5, where t is the time (in seconds) since the object was launched. For how many seconds is the object at or above a height of 25 meters? 11. A model rocket is launched from the top of a building. The height (in meters) of the rocket above the ground is given by h(t) = -61 + 24t + 14, where t is the time (in seconds) since the rocket was launched. What is the rocket's maximum height? 12. Determine the following characteristics for the function: y = - 2x' + 8x + 1 a.) Is the function given in intercept e.) x-intercept(s): i.) Graph the function. form, standard form, or vertex form? Circle your answer. y-intercept(s): b.) Line/Axis of Symmetry f.) Using interval notation, describe where the function is increasing and decreasing. c.) Vertex g.) Using interval notation, describe the domain of the function. d.) Does the function have a h.) Using interval notation, describe the maximum or a minimum? Circle range of the function. your answer. What is the max/min value? ( Unit Two Page 12