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

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
.
Cancel out the x and then multiply negative Start Fraction 1 over 2 End Fraction and negative 20 .

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

Answer 1

To find the horizontal distance the ball has traveled when the height of the soccer ball equals 0, Leon can use the Zero Product Property. Here's how:

The equation is set to 0:

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

According to the Zero Product Property, if the product of two factors equals zero, then at least one of the factors must equal zero. Thus, he can set each factor equal to zero:

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

Now, solve the two equations:

1. From \(-12x = 0\), we can simplify to: \[ x = 0 \]

2. From \(x - 20 = 0\), we can solve for \(x\) as follows: \[ x = 20 \]

Thus, Leon finds the values of \(x\) where the height \(h(x) = 0\):

• \(x = 0\) (initial point when the ball is kicked)
• \(x = 20\) (when the ball hits the ground)

So, the correct response is:

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