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 have traveled
yards before hitting the ground.

Answer 1

Use the table to answer the question.

(x+3)(x+4)=0
x−3=0
x+4=0
x=3
x=−4
While using the Zero Product Property to find the values of x that make the quadratic equation (x+3)(x+4)
equals 0, Oliver completed the work provided in the table. Is Oliver’s work accurate?(1 point)
Responses

No, x+4=0
in the second row should be x−4=0
.
No, x plus 4 equals 0 in the second row should be x minus 4 equals 0 .

Yes, the work is accurate.
Yes, the work is accurate.

No, he should have a third column where he should set x=0
.
No, he should have a third column where he should set x equals 0 .

No, x−3=0
in the second row should be x+3=0
.

Answer 2

To determine how far the ball will have traveled when it hits the ground, we need to solve the equation:

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

This equation is set to zero because we're interested in the height \( h(x) \) of the football being zero, which is when it hits the ground.

First, we can set the equation equal to zero and factor it:

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

For this product to equal zero, either factor must be zero:

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

So the possible solutions for \( x \) are:

1. \( x = 0 \) (the starting point of the kick)
2. \( x = 61 \) (the point where the ball hits the ground)

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

Therefore, the answer is:

**61 yards**.