Question

The path of a soccer ball can be modeled by the equation h(x)=−
1
2

x(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 travels when it hits the ground, we need to find the value of \( x \) when the height \( h(x) \) is equal to 0 (the ground level).

The equation given is:

\[
h(x) = -\frac{1}{2} x(x - 20)
\]

Setting \( h(x) = 0 \):

\[
-\frac{1}{2} x(x - 20) = 0
\]

This equation can be factored as follows:

\[
-\frac{1}{2} x(x - 20) = 0
\]

By setting each factor equal to zero:

1. \( x = 0 \) (This is when the ball is kicked from the ground.)
2. \( x - 20 = 0 \) (This gives \( x = 20 \).)

Thus, when \( x = 20 \) feet, the ball will hit the ground.

The horizontal distance the ball travels when it hits the ground is:

\[
\text{20 feet}
\]