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:

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

This equation is a product of two factors set equal to zero, so we can set each factor equal to zero:

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

From the first factor:

\[ -130x = 0 \]
\[ x = 0 \]

From the second factor:

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

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

Since \( x = 0 \) represents the starting point of the kick, the ball will have traveled **61 yards** before hitting the ground.

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