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

Cancel out the x and then multiply −1/2 and −20


Solve the two equations: −1/2x=0 and x−20=0
Plug in 0 for all the x terms in the function

Answer 1

Leon can use the Zero Product Property to find the horizontal distance the ball has traveled when the height of the soccer ball equals 0 by setting each factor of the equation \( 0 = -\frac{1}{2}x(x-20) \) to zero.

The equation can be factored as:
\[
-\frac{1}{2}x(x - 20) = 0
\]

To apply the Zero Product Property, we can break this down into two equations:
1. \(-\frac{1}{2}x = 0\)
2. \(x - 20 = 0\)

Now, we solve each equation:

1. From \(-\frac{1}{2}x = 0\):
\[
x = 0
\]

2. From \(x - 20 = 0\):
\[
x = 20
\]

Thus, Leon can find that the horizontal distances at which the height of the soccer ball equals 0 are \(x = 0\) (the starting point) and \(x = 20\) (when the ball hits the ground).

Therefore, the answer is to **solve the two equations: −1/2x=0 and x−20=0**.