The path of a soccer ball can be modeled by the equation h(x)=−12x(x−20)

Question

, 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 .

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 .

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.
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Answer 1

To find the horizontal distance the ball has traveled when the height \( h(x) \) equals 0, Leon can use the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

From the equation:

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

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

Hence, the ball hits the ground when \( x = 0 \) (the starting point) and \( x = 20 \) (the point where it hits the ground).

So, the correct response is:

Solve the two equations: \( -12x=0 \) and \( x−20=0 \).