Question

The path of a soccer ball can be modeled by the equation h(x)=−12x(x−20)
, where h(x) is the height of the ball, and x is the horizontal distance the ball has traveled. To determine how far the ball has traveled when it hits the ground, Leon set the height equal to 0 and obtained the equation: 0=−12x(x−20)
. How can he use the Zero Product Property to find the horizontal distance the ball has traveled when the height of the soccer ball equals 0?(1 point)

He cannot use the Zero Product Property because the height will never be 0.

Cancel out the x and then multiply −12
and −20
.

Plug in 0 for all the x terms in the function.

Solve the two equations: −12x=0
and x−20=0
.
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Answer 1

Use the Zero Product Property: if a product is 0, at least one factor is 0. From 0 = −12x(x−20) set the factors equal to 0:

-12x = 0 → x = 0
x − 20 = 0 → x = 20

So the ball is on the ground at x = 0 (kick point) and x = 20 (where it lands). The horizontal distance traveled before landing is 20 units.