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

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

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

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

Answer 1

To find the horizontal distance the ball has traveled when the height is equal to 0 using the Zero Product Property, Leon should solve the equation:

\[ 0 = -12x(x - 20) \]

By the Zero Product Property, if the product of two factors is zero, at least one of the factors must be zero. Therefore, he can set each factor equal to zero:

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

Now, solving these equations:

1. For \(-12x = 0\):
\[
x = 0
\]

2. For \(x - 20 = 0\):
\[
x = 20
\]

Thus, the horizontal distances where the height is 0 are \(x = 0\) and \(x = 20\). This means the ball hits the ground at these two points (when it is kicked and when it lands).

Therefore, the correct response is:

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