Question

The path of a soccer ball can be modeled by the equation h(x)=−1/2x(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=−1/2x(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

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 .

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 .

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.

Plug in 0 for all the x terms in the function.
Plug in 0 for all the x terms in the function.
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Answer 1

To use the Zero Product Property to find the horizontal distance the ball has traveled when the height of the soccer ball equals 0, Leon should set each factor of the equation \(0 = -\frac{1}{2}x(x - 20)\) to zero. This means he has two equations to solve:

1. \(-\frac{1}{2}x = 0\)
2. \(x - 20 = 0\)

When he sets each factor equal to zero:

1. From \(-\frac{1}{2}x = 0\), solving for \(x\) gives \(x = 0\).
2. From \(x - 20 = 0\), solving for \(x\) gives \(x = 20\).

Thus, the ball hits the ground when \(x = 0\) (the starting point) or \(x = 20\) (the point where it lands after being kicked). The correct response to the question would be:

**Solve the two equations: -\frac{1}{2}x = 0 and x - 20 = 0.**