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 blank yards before hitting the ground.

Answer 1

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

Given the equation:

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

This equation can be factored to find the roots:

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

To find the values of \( x \) where the height \( h(x) \) is zero, we set the factors equal to zero:

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

From the first factor:

\[
x = 0
\]

From the second factor:

\[
x - 61 = 0 \implies x = 61
\]

The solutions to the equation are \( x = 0 \) and \( x = 61 \).

The \( x = 0 \) corresponds to the initial point of the kick-off (the starting position of the football), while \( x = 61 \) represents the horizontal distance when the ball hits the ground.

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