Frank hit a golf ball from the top of a hill. The height of the ball above the green is given in the table below. Determine the equation of the polynomial regression that best models this data. Use the regression to determine the following.

  1. The time when the ball is at a height of 70 metres.
  2. The maximum height of the ball.

Time (min)
1
2
3
4
5
Height (m)
52.5
73.2
74.6
55.8
16.1

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

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

  1. To find the time when the ball is at a height of 70 metres means to find x when y = 70.

Step 1: Input the given y-value; press Y =, down arrow to scroll to Y2 =, 70.

Step 2: Graph the functions; press GRAPH.

Step 3: Find the first intersection point; press 2nd, TRACE, 5, ENTER, ENTER, ENTER.

Step 4: Find the second intersection point; press 2nd, TRACE, 5, left arrow to scroll to the second intersection point, ENTER, ENTER, ENTER.

The golf ball will be at a height of 70 metres after approximately 1.74 seconds and 3.36 seconds.

  1. The calculator has a feature specifically for finding the maximum value on a curve.

Step 1: Clear all unnecessary functions; press Y = then, CLEAR for each function that needs deleting. Do not clear the quadratic regression.

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

Step 3: Find maximum; press 4, left arrow to scroll to the left of the maximum point, ENTER, right arrow to scroll to the right of the maximum point, ENTER, ENTER.

The maximum height of the ball is approximately 76.6 metres.