Question

To begin a football game, a kicker has to kick off. The football follows the path h(x)=−1/30x(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=−1/30x(x−61)


(1 point)
The ball will h

Answer 1

To determine how far the football will have traveled when it hits the ground, we need to set the height \( h(x) \) equal to zero and solve for \( x \). The function given is:

\[
h(x) = -\frac{1}{30}x(x-61)
\]

Setting it equal to zero:

\[
0 = -\frac{1}{30}x(x-61)
\]

To solve this equation, we can multiply both sides by -30 (to eliminate the fraction):

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

Now we can factor the equation:

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

Setting each factor equal to zero gives us:

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

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

In the context of the football's path, \( x = 0 \) represents the point where the ball is kicked from, and \( x = 61 \) represents the point where the ball hits the ground.

Therefore, the ball will have traveled **61 yards** when it hits the ground.