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

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 .

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

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.

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 set each factor in the equation equal to zero. The equation he has is:

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

According to the Zero Product Property, if the product of two factors equals zero, then at least one of the factors must be equal to zero.

This gives us two equations to solve:

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

From these, we can solve for \(x\):

1. From \(-12x = 0\), dividing both sides by \(-12\) gives \(x = 0\).
2. From \(x - 20 = 0\), adding 20 to both sides gives \(x = 20\).

So, the ball has traveled a horizontal distance of \(0\) and \(20\) when the height is \(0\) (when it hits the ground).

Thus, the correct response is:

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