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 .

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

He

Answer 1

To solve the equation \( 0 = -12x(x - 20) \) using the Zero Product Property, Leon should recognize that if the product of two factors equals zero, then at least one of the factors must equal zero.

The equation can be factored into two parts:
1. \( -12x = 0 \)
2. \( (x - 20) = 0 \)

Setting each factor equal to zero gives:

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

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

Thus, the solutions are \( x = 0 \) and \( x = 20 \). These represent the horizontal distances where the ball hits the ground: at the starting point (0) and when it lands again (20).

Therefore, Leon can use the Zero Product Property to find that the ball has traveled a horizontal distance of 20 units when it hits the ground for the second time.

The correct response based on the options is not explicitly listed, but the Zero Product Property helps Leon find that the horizontal distances are \( x = 0 \) and \( x = 20 \).