Practice problem 1: Suppose that a golf ball travels a distance of 600 feet as measured along the ground and reaches an altitude of 200 feet. If the origin represents the tee and the ball travels along a parabolic path that opens downward, find an equation for the path of the golf ball.


We are given that the path is a parabola and we assume that the landing point is 600 feet away from the tee at the same elevation.

Since it is a parabola. if we let the level ground represent the x-axis, the path with have an equation of the form

If we know three (x, y) points along the path, we can substitute each of the three for x and y in this equation and get a system of equations which we can solve for a, b, and c.    


Three points: (0, 0) for the tee, (300, 200) for high point of the path, and (600, 0) for the landing spot. Do we need to argue that the midpoint of the distance travelled (300 feet) will also be where the ball reaches its highest elevation (200 feet)? We get a system of equations in a, b, and c.

Equation Graphed with Graphing Calculator 4.0 (Web link)

GCF (Application)