Question

The Zero Product Property Practice
Complete this assessment to review what you’ve learned. It will not count toward your grade.
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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.
Remaining Attempts : 3

Answer 1

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

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

Using the Zero Product Property, we set each factor equal to zero:

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

**From the first equation:**
\[
-130x = 0 \implies x = 0
\]

**From the second equation:**
\[
x - 61 = 0 \implies x = 61
\]

So the two solutions are \( x = 0 \) and \( x = 61 \).

**Interpretation:**
- \( x = 0 \) represents the point at which the ball is kicked (the starting point).
- \( x = 61 \) represents the point where the ball hits the ground.

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