To begin a football game, a kicker has to kick off. The football follows the path h(x)=−130x(x−61)

Question

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: $$\boxed{{\displaystyle 61}}\text{ yards}$$ before hitting the ground.