The Football Problem
Troy Aikman is standing on the 40-yard line of the Pittsburgh Steelers. He throws a pass toward
their end zone. The ball is 2 yards above the ground when he lets it go. It follows a parabolic
path reaching its highest point, 14 yards above the ground, as it crosses the 20-yard line. In
answering the following questions, let x be the number of yards from the goal line, and let y be
the number of yards the ball is above the ground.
1.
2.
3.
4.
5.
6.
7.
8.
On a separate page, sketch a picture of the path of the ball above the football field.
Place the coordinates of the following on your picture:
a.
the point from which the ball is thrown
b.
its maximum height
c.
the point at which it is caught (for purposes of the problem, the ball is caught at a
point which is symmetrical to the point from which it is thrown )
Using the appropriate features of the graphing calculator to input the x coordinates and y
coordinates of your data, construct a scatter plot and find the equation of the quadratic
regression which fits this data. Record your equation below.
Use the graphing calculator to graph the equation. State your viewing window.
How high is the ball when it crosses the 10-yard line? Explain your answer.
If nobody catches the ball, where will it hit the ground? Explain your answer.
State a reasonable domain and range for this problem. Explain your answer.
Draw the graph of the function in a reasonable domain and label significant points.
Charles A. Dana Center
Mathematics TEKS Toolkit
www.mathtekstoolkit.org