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

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.
He cannot use the Zero Product Property because the height will never be 0.

Solve the two equations: −12x=0 and x−20=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 can set each factor in the equation \(0 = -12x(x - 20)\) to zero. This gives us two equations to solve:

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

From these equations, he can find the values of \(x\):

1. For \(-12x = 0\), dividing both sides by -12 gives \(x = 0\).
2. For \(x - 20 = 0\), solving for \(x\) gives \(x = 20\).

Thus, the horizontal distances when the height is 0 are \(x = 0\) and \(x = 20\). This means the ball hits the ground at two points: when it was initially kicked (0 distance) and when it lands after traveling 20 units horizontally.

So the correct response is:

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