In Exercises 1–4, the graph of a quadratic function is given. Write the function’s equation, selecting from the following options.
1.
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COLLEGE ALGEBRA ESSENTIALS
- The function f(x) = 0.4x2 – 36x + 1000 models the number of accidents, f(x), per 50 million miles driven as a function of a driver's age, x, in years, for drivers from ages 16 through 74, inclusive. The graph of f is shown. Use the equation for f to solve Exercises 45–48. 1000 flx) = 0.4x2 – 36x + 1000 16 45 74 Age of Driver 45. Find and interpret f(20). Identify this information as a point on the graph of f. 46. Find and interpret f(50). Identify this information as a point on the graph of f. 47. For what value of x does the graph reach its lowest point? Use the equation for f to find the minimum value of y. Describe the practical significance of this minimum value. 48. Use the graph to identify two different ages for which drivers have the same number of accidents. Use the equation for f to find the number of accidents for drivers at each of these ages. Number of Accidents (per 50 million miles)arrow_forwardGraph the standard quadratic function, f(x) = x2. Then use transformations of this graph to graph the given function h(x) = (x - 2)2 + 1arrow_forwardWrite the quadratic function in f(x) = a(x − h)2 + k form whose points on the graph are (-1,-5) and (0,-4)arrow_forward
- the quadratic function which describes the given graph is f(x)=arrow_forwardWrite a function for the blue graph of a quadratic function in a form: f(x) = a (b (x + c))2 + d (1, 1). (0,0) 2 (0, –1) (-1, –3)arrow_forwardThe Mauna Loa Observatory in Hawaii records the carbon dioxide concentration y (in parts per million) in Earth’s atmosphere. The January readings for various years are shown in Figure . In the July 1990 issue of Scientific American, these data were used to predict the carbon dioxide level in Earth’s atmosphere in the year 2035, using the quadratic model y = 0.018t2 + 0.70t + 316.2 (Quadratic model for 1960–1990 data) where t = 0 represents 1960, as shown in Figure a. The data shown in figure b represent the years 1980 through 2014 and can be modeled by y = 0.014t2 + 0.66t + 320.3 (Quadratic model for 1980–2014) data where t = 0 represents 1960. What was the prediction given in the Scientific American article in 1990? Given the second model for 1980 through 2014, does this prediction for the year 2035 seem accurate?arrow_forward
- Graph the function G(x) = x2 +6x + 1arrow_forwardIn Exercises 31–32, each function is defined by two equations. The equation in the first row gives the output for negative numbers in the domain. The equation in the second row gives the output for nonnegative numbers in the domain. Find the indicated function values. S3x + 5 ifx 0 31. f(x) = а. f(-2) b. f(0) с. f(3) d. f(-100) + f(100)arrow_forwardThe table shows fuel consumption (in billions of gallons) by all non-military motor vehicles in selected years. Let x = 0 correspond to 1970. Using (5,102.0) as the vertex and the data for 1990, find a quadratic function f(x) = a(x - h) + k that models this data. Use the model to estimate fuel consumption in 1992. What is the quadratic function that models the data? f(x) = D (x -D2 +O Year Fuel Consumption (Round to three decimal places as needed.) 1975 102.0 1980 104.5 1985 110.9 1990 119.8arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning