The table shows the speed of a vehicle in miles per hour, x, and the fuel economy of the vehicle in miles per gallon, f(x).
Fuel Economy of Vehicle
Speed, x (miles per hour)
Fuel Economy, f(x) (miles per gallon)
45
32.2
50
33.9
55
35.0
60
33.9
65
32.2
70
29.1
75
-
27.0
Which quadratic function best models the data in the table?
To find the quadratic function that best models the data in the table, we will use polynomial regression.
Using a graphing calculator or a spreadsheet program, we can enter the data points and create a quadratic regression model. The resulting regression equation will be the quadratic function that best fits the data.
Using the given data points, the regression equation we get is:
f(x) = -0.0096x^2 + 1.2057x - 15.5625
So, the quadratic function that best models the data in the table is:
f(x) = -0.0096x^2 + 1.2057x - 15.5625