Use the regression model and graph from Example 1 to find the - and -intercepts of the graph. Interpret their meanings. Then, use the equation to predict the car’s fuel efficiency at the speeds of mph, mph, mph, and mph. Determine whether each of these predictions is an interpolation or an extrapolation, and whether any of the predictions seem unreasonable within the context of the problem.
The data table from Example 1 (lower right) shows a car’s speed in miles per hour and the car’s fuel efficiency in miles per gallon for each speed.
A quadratic regression equation that models this data is given by , where is speed in mph and is fuel efficiency in mpg. A scatter plot of the data with the graph of this model is shown.

Find the -intercepts of the graph.

Interpret the meaning of the -intercepts.

Find the -intercept.

Interpret the meaning of the -intercept.

Use the equation to predict the fuel efficiency at the speeds of mph, mph, mph, and mph. Determine whether each of these predictions is an interpolation or an extrapolation, and if any of the predictions seem unreasonable within the context of the problem.