Question

To begin a football game, a kicker has to kick off. The football follows the path h(x)=−130x(x−61)
, where h(x)
is the height of the football and x is the horizontal distance it has traveled in yards. Solve the equation to determine how far the ball will have traveled when it hits the ground.

0=−130x(x−61)


(1 point)
The ball will have traveled
yards before hitting the ground.

Answer 1

To determine how far the ball will have traveled when it hits the ground, we need to solve the equation \( h(x) = 0 \).

The equation is given by:

\[
0 = -130x(x - 61)
\]

We can start by factoring out the common term:

\[
0 = -130x(x - 61)
\]

Setting each factor equal to zero gives us:

1. \( -130x = 0 \)
2. \( x - 61 = 0 \)

From the first equation, we find:

\[
x = 0
\]

From the second equation, we find:

\[
x = 61
\]

Thus, the two solutions to the equation \( h(x) = 0 \) are \( x = 0 \) and \( x = 61 \).

The ball will have traveled **61 yards** before hitting the ground.

Therefore, the final answer is:

**61 yards**.