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)

Question

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 .

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 .

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

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.

Answer 1

To find the horizontal distance the ball has traveled when the height is 0, Leon can apply the Zero Product Property to the equation \( 0 = -12x(x - 20) \).

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

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

From the first equation, \(-12x = 0\) gives: \[ x = 0 \]

From the second equation, \(x - 20 = 0\) gives: \[ x = 20 \]

Thus, the two solutions for \(x\) are \(0\) and \(20\). This means the ball hits the ground when it has traveled \(0\) units (at the moment it is kicked) and \(20\) units (when it lands).

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