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

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 .

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.

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 .
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Answer 1

To find the horizontal distance the ball has traveled when the height of the soccer ball equals 0 using the Zero Product Property, Leon should follow these steps:

1. Set the height equation equal to 0:
   \( 0 = -12x(x - 20) \)

2. Apply the Zero Product Property, which states that if the product of two factors is zero, at least one of the factors must be zero. This gives us two equations to solve:

   • \( -12x = 0 \)
   • \( x - 20 = 0 \)

3. Solving these equations:

   • For \( -12x = 0 \), dividing both sides by -12 gives \( x = 0 \).
   • For \( x - 20 = 0 \), adding 20 to both sides gives \( x = 20 \).

Therefore, the horizontal distances when the height is 0 are \( x = 0 \) and \( x = 20 \).

The correct response is: Solve the two equations: −12x=0 and x−20=0.