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Question

A football is kicked toward a goal post that is 10 feet high. The path of the football is modeled by the graph of y = -0.005x^2 + 0.6x where x and y are measured in feet. On a coordinate plane, the x-axis represents the ground, and the ball leaves the ground at the origin. The ball hits the goal post on the way down. How far from the goal post is the kicker? Explain.

Answer 1

Set the original equation equal to 10, then solve for x.

0.005x^2+0.6x=10

0.005x^2+0.6x-10=0

use the quadratic formula to find the roots.

x=20 or 100

since it says that the ball hits on the way down, we use the larger number.

So, the kicker is 100 feet from the goal post