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

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.
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.

Answer 1

To determine how far the soccer ball has traveled when it hits the ground, Leon correctly set the height \( h(x) \) equal to 0, resulting in the equation:

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

To use the Zero Product Property, we recognize that for the product of two factors to equal zero, at least one of the factors must be equal to zero. This gives us two equations to solve:

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

Now, we can solve each equation:

1. From \( -12x = 0 \), we can divide both sides by -12: \[ x = 0 \]

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

Thus, the horizontal distances where the height of the soccer ball equals 0 (where it hits the ground) are \( x = 0 \) and \( x = 20 \).

The correct response to the question is:

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