The Zero Product Property Practice

Question

Complete this assessment to review what you’ve learned. It will not count toward your grade.
5 of 55 of 5 Items

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.