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)

Question

1. He cannot use the Zero Product Property because the height will never be 0
2. Solve the two equations: −1/2x=0 and x−20=0
3. Plug in 0 for all the x terms in the function
4. Cancel out the x and then multiply −1/2 and −20.

Answer 1

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

In the equation \(0 = -\frac{1}{2}x(x - 20)\), he can set each factor equal to zero:

1. The first factor is \(-\frac{1}{2}x\). Setting this equal to zero, we have: \[ -\frac{1}{2}x = 0 \implies x = 0. \]

2. The second factor is \(x - 20\). Setting this equal to zero, we have: \[ x - 20 = 0 \implies x = 20. \]

Thus, the solutions to the equation \(0 = -\frac{1}{2}x(x - 20)\) are \(x = 0\) and \(x = 20\).

So, the correct answer is:

2. Solve the two equations: −1/2x=0 and x−20=0.