The Zero Product Property Quick Check

Question

3 of 53 of 5 Items

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)
Responses

Solve the two equations: −12x=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.

Cancel out the x and then multiply −12 and −20.
Cancel out the x and then multiply negative Start Fraction 1 over 2 End Fraction and negative 20 .

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

Answer 1

To use the Zero Product Property to find the horizontal distance the ball has traveled when the height \( h(x) \) equals 0, Leon can set each factor of the equation \( 0 = -12x(x - 20) \) equal to zero.

This leads to the two equations:

1. \( -12x = 0 \)
2. \( x - 20 = 0 \)

From the first equation, \( x = 0 \) (which indicates the starting point when the ball is kicked), and from the second equation, \( x = 20 \) (which indicates the point where the ball hits the ground).

Therefore, the correct response is: Solve the two equations: −12x=0 and x−20=0.