448 Chapter 8Graphing Quadratic Functions 63. MODELING WITH MATHEMATICS A portion of a roller coaster track is in the shape of a parabola. Write and graph a quadratic function that models this portion of the roller coaster with a maximum height of 90 feet, represented by a vertex of (25, 90), passing through the point (50, 0). (See Example 5.) 64. MODELING WITH MATHEMATICS A are is launched from a boat and travels in a parabolic path until reaching the water. Write and graph a quadratic function that models the path of the are with a maximum height of 300 meters, represented by a vertex of (59, 300), landing in the water at the point(119, 0).In Exercises 65–68, rewrite the quadratic function in vertex form. 65. y 2x2 8x + 4 66. y 3x2 + 6x 1 67.f (x) 5x2 + 10x + 368. f (x) x2 4x + 2 69. REASONING Can a function be symmetric about the x-axis? Explain. 70. HOW DO YOU SEE IT? The graph of a quadratic function is shown. Determine which symbols to use to complete the vertex form of the quadratic function. Explain your reasoning.242x6423y y a(x 2)2 3In Exercises 71–74, describe the transformation from the graph of f to the graph of h. Write an equation that represents h in terms of x.71. f (x) (x + 1)2 2 72. f (x) 2(x 1)2 + 1h(x) f (x) + 4 h(x) f (x 5)73. f (x) 4(x 2)2 + 3 74. f (x) (x + 5)2 6h(x) 2f (x) h(x) 1 — 3 f (x) 75. REASONING The graph of y x2 is translated 2unitsright and 5 units down. Write an equation for the function in vertex form and in standard form. Describeadvantages of writing the function in eachform. 76. THOUGHT PROVOKING Which of the following are true? Justify your answers. a. Any constant multiple of an even function is even. b. Any constant multiple of an odd function is odd. c. The sum or difference of two even functions is even. d. The sum or difference of two odd functions is odd. e. The sum or difference of an even function and an odd function is odd. 77. COMPARING FUNCTIONS A cross section of a birdbath can be modeled by y 1 — 81 (x 18)2 4, where x and y are measured in inches. The graph shows the cross section of another birdbath.xy81624332
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48816162424yy x2 x 27545 a. Which birdbath is deeper? Explain. b. Which birdbath is wider? Explain. 78. REASONING Compare the graphs of y 2x2 + 8x +8 and y x2 without graphing the functions. How can factoring help you compare the parabolas? Explain. 79. MAKING AN ARGUMENT Your friend says all absolute value functions are even because of their symmetry. Is your friend correct? Explain.Maintaining Mathematical ProficiencyMaintaining Mathematical ProficiencySolve the equation.(Section 7.4) 80. x(x 1) 0 81. (x + 3)(x 8) 0 82. (3x 9)(4x + 12) 0Reviewing what you learned in previous grades and lessons