Question

A football player attempts to kick a football across a field. The path of the football can be modeled by the function h(x) = − 1/225 x^2 + 2/3 x, where x is the horizontal distance from the kick, and h(x) is the height of the football above the ground, when both are measured in feet. How far from the kicker will the football land?

Answer 1

Answer :
1+ 150 -
225x

Answer 2

The football will land 150 feet from the kicker.

How to find the horizontal distance

To find the horizontal distance at which the football lands, you need to determine the x-value when the height function h(x) = 0.

h(x) = − 1/225 x² + 2/3 x = 0

− 1/225 x² + 2/3 x = 0

To make the equation easier to work with, you can multiply both sides by 225 to eliminate the fraction:

-x² + 150x = 0\]

-x(x - 150) = 0

x = 0 OR x = 150

This equation has two solutions: x = 0 and x = 150

Therefore, the football will land 150 feet from the kicker.