466 Chapter 8Graphing Quadratic Functions19. MODELING WITH MATHEMATICS A student takes a subway to a public library. The table shows the distances d (in miles) the student travels in t minutes. Let the time t represent the independent variable. Tell whether the data can be modeled by a linear, an exponential, or a quadratic function. Explain.Time, t0.5135Distance, d0.3350.672.013.3520. MODELING WITH MATHEMATICS A store sells custom circular rugs. The table shows the costs c (in dollars) of rugs that have diameters of d feet. Let the diameter d represent the independent variable. Tell whether the data can be modeled by a linear,an exponential, or a quadratic function. Explain.Diameter, d3456Cost, c63.90113.60177.50255.60In Exercises 21–26, tell whether the data represent a linear, an exponential, or a quadratic function. Then write the function. (See Example 3.)21. (2, 8), (1, 0), (0, 4), (1, 4), (2, 0), (3, 8)22. (3, 8), (2, 4), (1, 2), (0, 1), (1, 0.5)23. x21012y4125824. x10123y2.5510204025. 26. 4282x24y12242x24y2427. ERROR ANALYSIS Describe and correct the error in determining whether the table represents a linear, an exponential, or a quadratic function.+ 1× 3+ 1× 3+ 1+ 1× 3× 3x12345y392781243Consecutive y-values change by a constant amount. So, the table represents a linear function.✗
28. ERROR ANALYSIS Describe and correct the error in writing the function represented by the table. x32101y40220+ 1 4+ 1 2+ 2+ 1+ 1+ 0+ 2+ 2+ 2first differencessecond differencesThe table represents a quadratic function.f (x) = a(x − 2)(x − 1)4 = a(−3 − 2)(−3 − 1) 1 — 5 = af (x) = 1 — 5 (x − 2)(x − 1) = 1 — 5 x2 − 3 — 5 x 2 — 5 So, the function is f (x) = 1 — 5 x2 − 3 — 5 x 2 — 5 .✗
29. REASONING The table shows the numbers ofpeople attending the rst vefootball games at a high school.Game, g12345People, p252325270249310a. Plot the points. Let the game g represent the independent variable.b. Can a linear, an exponential, or a quadratic function represent this situation? Explain.