To this point in the lesson, you have learned how to determine the best polynomial regression function to model a set of data. The remainder of this lesson focuses on using the polynomial regression to solve problems.

 Nicola recorded odometer measurements during a single trip in her car. The data she collected is shown in the table below. Construct a scatter plot for the data, and determine the best regression model for the data. Use your model to find the following. The possible distance travelled in 45 mintues. The time Nicola took to travel 25 kilometres.

 Time (min) 2 6 10 13 14 19 23 35 40 Distance (km) 2 5 8 10 11 15 18 26 31

Graph the data using Steps 1 to 7 as shown in Examples 1 to 4. Place time in L1 and distance in L2.

Graph the regression model using Steps 8 to 11 as shown in Examples 1 to 4.

1. To find the possible distance travelled in 45 minutes means to find y when x = 45, and this is accomplished in the following steps.

Step 1: Go to the CALCULATE menu; press 2nd, TRACE.

Step 2: Select value; press 1.

Step 3: Type in the required x-value; press 45.

Step 4: Get the corresponding y-value; press ENTER.

The distance travelled in 45 minutes is approximately 34.27 kilometres.

1. To find the time Nicola took to travel 25 kilometres means to find x when y = 25. Although several ways to find this answer are possible, the most accurate method is shown in the steps that follow.

Step 1: Input the given y-value; press Y=, down arrow to scroll to Y2, 25.

Step 2: Gaph the functions; press GRAPH.

Step 3: Go to the CALCULATE menu; press 2nd, TRACE.

Step 4: Find the intersection of Y1 and Y2; press 5, ENTER, ENTER, ENTER.

Nicola takes approximately 32.65 minutes to drive 25 kilometres.