Question

A) The path of a soccer ball can be modeled by the equation \(h\left(x\right)=-\frac{1}{2}x\left(x20\right)\), where \(h\left(x\right)\) 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 find the horizontal distance the soccer ball has traveled when it hits the ground, we need to determine when the height \( h(x) \) is equal to zero. The equation given is:

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

We set \( h(x) = 0 \):

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

This equation can be solved by factoring. The factors of the equation are:

\[
-\frac{1}{2}x = 0 \quad \text{or} \quad x - 20 = 0
\]

Setting each part to zero gives:

1. \(-\frac{1}{2}x = 0\) leads to \(x = 0\) (the point where the ball starts).
2. \(x - 20 = 0\) leads to \(x = 20\) (the point where the ball hits the ground again).

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

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