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

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

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.

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 find the horizontal distance the ball has traveled when it hits the ground using the Zero Product Property, Leon can set the height equation to zero:

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

According to the Zero Product Property, if the product of two factors is equal to zero, then at least one of the factors must be zero. Therefore, Leon can set each factor equal to zero:

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

Solving these equations:

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

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

Thus, the solutions to the equation are \(x = 0\) and \(x = 20\), meaning the ball is at a height of 0 at these two horizontal distances.

So, the correct response to the question would be:

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