Question

The path of a soccer ball can be modeled by the equation h(x)=−12x(x−20)
, where h(x)
is the height reached by the ball, in feet, and x is the horizontal distance the ball has traveled, in feet. What is the horizontal distance the ball will have traveled when it hits the ground? Use a graph or table if necessary.(1 point)
The ball will have traveled a horizontal distance of
feet when it hits the ground.

Answer 1

To determine the horizontal distance the ball will have traveled when it hits the ground, we need to find the values of \( x \) for which the height \( h(x) \) is 0. The equation given is

\[
h(x) = -12x(x - 20).
\]

Setting \( h(x) \) to 0 to find the x-intercepts:

\[
-12x(x - 20) = 0.
\]

This equation can be factored as:

\[
-12x = 0 \quad \text{or} \quad (x - 20) = 0.
\]

Solving for \( x \):

1. From \( -12x = 0 \), we get:
\[
x = 0.
\]

2. From \( x - 20 = 0 \), we get:
\[
x = 20.
\]

Thus, the ball hits the ground at \( x = 0 \) and \( x = 20 \). The first solution (0) refers to the point where the ball was kicked, and the second solution (20) is the point where the ball returns to the ground.

Therefore, the horizontal distance the ball will have traveled when it hits the ground is

\[
\boxed{20} \text{ feet}.
\]