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 .

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.
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.

Answer 1

To determine how far the soccer ball has traveled when it hits the ground, Leon can use the Zero Product Property. This property states that if the product of two factors equals zero, then at least one of the factors must be zero.

Given the equation:

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

Leon can set each factor equal to zero:

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

Now he can solve these equations:

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

Thus, the two solutions to the equation are \( x = 0 \) and \( x = 20 \).

To summarize, Leon can use the Zero Product Property to find the horizontal distance the ball has traveled when it hits the ground by solving the two equations: \( -12x = 0 \) and \( x - 20 = 0 \).

So the correct choice is:

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