The path of a soccer ball can be modeled by the equation h (x) = - 2x (x - 20), where

Question

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 = - ½ x 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 O?
(1 point)
• He cannot use the Zero Product Property because the height will never be O.
• Plug in 0 for all the x terms in the function.
• Cancel out the x and then multiply and —20.
• Solve the two equations: - ½ x = 0 and x - 20 = 0.

Answer 1

To determine when the height of the soccer ball is equal to zero, we start from the equation:

\[ h(x) = -2x(x - 20) \]

Setting this equal to zero gives:

\[ -2x(x - 20) = 0 \]

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

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

Now let's analyze your options for how Leon can use the Zero Product Property to find the horizontal distance:

• He cannot use the Zero Product Property because the height will never be O. (Incorrect, as we demonstrated that the height can indeed be zero.)
• Plug in 0 for all the x terms in the function. (Incorrect, as this does not utilize the Zero Product Property correctly.)
• Cancel out the x and then multiply and —20. (Incorrect, as this doesn't apply the Zero Product Property properly.)
• Solve the two equations: -2x = 0 and x - 20 = 0. (Correct, as this correctly uses the Zero Product Property to separate the factors and solve for x.)

Thus, the correct choice from the options provided is:

Solve the two equations: -2x = 0 and x - 20 = 0.