Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop-and-go traffic. At higher speeds, the car must overcome more wind resistance. The variable x given in the table represents the speed (in mph) for a compact car, and m(x) represents the gas mileage (in mpg). 25 30 35 40 45 т(x) 22.7 25.1 27.9 30.8 31.9 50 55 60 65 т(x) 30.9 28.4 24.2 21.9 a. Use regression to find a quadratic function to model the data. b. At what speed is the gas mileage the greatest? Round to the nearest mile per hour. c. What is the maximum gas mileage? Round to the nearest mile per gallon.

Question
Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop-and-go traffic.
At higher speeds, the car must overcome more wind resistance. The variable x given in the table represents the speed (in
mph) for a compact car, and m(x) represents the gas mileage (in mpg).
25
30
35
40
45
т(x)
22.7
25.1
27.9
30.8
31.9
50
55
60
65
т(x)
30.9
28.4
24.2
21.9
a. Use regression to find a quadratic function to model the data.
b. At what speed is the gas mileage the greatest? Round to the nearest mile per hour.
c. What is the maximum gas mileage? Round to the nearest mile per gallon.
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Transcribed Image Text

Gas mileage is tested for a car under different driving conditions. At lower speeds, the car is driven in stop-and-go traffic. At higher speeds, the car must overcome more wind resistance. The variable x given in the table represents the speed (in mph) for a compact car, and m(x) represents the gas mileage (in mpg). 25 30 35 40 45 т(x) 22.7 25.1 27.9 30.8 31.9 50 55 60 65 т(x) 30.9 28.4 24.2 21.9 a. Use regression to find a quadratic function to model the data. b. At what speed is the gas mileage the greatest? Round to the nearest mile per hour. c. What is the maximum gas mileage? Round to the nearest mile per gallon.