Question

To begin a football game, a kicker has to kick off. The football follows the path h(x)=−130x(x−61)
ℎ
(
𝑥
)
=
−
1
30
𝑥
(
𝑥
−
61
)
, where h(x)
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)
0
=
−
1
30
𝑥
(
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 set the height function \( h(x) \) equal to zero:

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

This equation can be solved by factoring:

1. Factor out \(-130\):
\[
0 = -130x(x - 61)
\]

This gives us two potential solutions:

1. \( x = 0 \)
2. \( x - 61 = 0 \) which simplifies to \( x = 61 \)

Thus, the ball will hit the ground at two positions:
- when \( x = 0 \) yards (which is the starting point)
- and when \( x = 61 \) yards.

Therefore, the ball will have traveled:
\[
\boxed{61} \text{ yards}
\]
before hitting the ground.