Question

The path of a soccer ball can be modeled by the equation h(x)=−1/2x(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=−1/2x(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)
Responses

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

Cancel out the x and then multiply −1/2
and −20
.
Cancel out the x and then multiply negative Start Fraction 1 over 2 End Fraction and negative 20 .

Solve the two equations: −1/2x=0
and x−20=0
.
Solve the two equations: negative Start Fraction 1 over 2 End Fraction x equals 0 and x minus 20 equals 0 .

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

Answer 1

Choose "Solve the two equations: −1/2x = 0 and x − 20 = 0."

By the Zero Product Property, set each factor equal to 0: −1/2x = 0 gives x = 0, and x − 20 = 0 gives x = 20. The ball hits the ground at x = 0 (launch) and x = 20, so it travels 20 units before landing.