335 3.1 Quadratic Functions and Models Connecting Graphs with Equations Find a quadratic function f having the graph shown. (Hint: See the Note following Example 3.) 51. x y (2, –1) (0, 0) 0 52. x y 0 (–2, 3) (0, –1) 53. x y (1, 4) (0, 2) 0 54. (1, 0) (–1, –12) x y 5 0 (Modeling) In each scatter diagram, determine whether a linear or a quadratic model is appropriate for the data. If linear, indicate whether the slope should be positive or negative. If quadratic, indicate whether the leading coefficient of x2 should be positive or negative. 55. number of shopping centers as a function of time 58. height of an object projected upward as a function of time 56. growth in science centers/museums as a function of time 59. Social Security assets as a function of time 57. value of U.S. salmon catch as a function of time 60. population of bacteria as a function of time (Modeling) Solve each problem. Give approximations to the nearest hundredth. See Example 5. 61. Height of a Toy Rocket A toy rocket (not internally powered) is launched straight up from the top of a building 50 ft tall at an initial velocity of 200 ft per sec. (a) Give the function that describes the height of the rocket in terms of time t. (b) Determine the time at which the rocket reaches its maximum height and the maximum height in feet. (c) For what time interval will the rocket be more than 300 ft above ground level? (d) After how many seconds will it hit the ground?
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