Question

The path of a soccer ball can be modeled by the equation
h
(
x
)
=
−
1
2
x
(
x
−
20
)
, where
h
(
x
) is theheight of the ball, and
x
is the horizontal distance the ball has traveled. To determine how far theball has traveled when it hits the ground, Leon set the height equal to 0 and obtained theequation:
0
=
−
1
2
x
(
x
−
20
)
. How can he use the Zero Product Property to find the horizontaldistance the ball has traveled when the height of the soccer ball equals 0?
(1 point)
Solve the two equations: −
1
2 x = 0 and x − 20 = 0.
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.
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 solving the equation he set up:

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

According to the Zero Product Property, if the product of two factors is zero, then at least one of the factors must be zero. Here, the factors are \(-\frac{1}{2}x\) and \((x - 20)\).

So, Leon can set up the two equations:

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

Now, solving these equations:

1. For \(-\frac{1}{2}x = 0\):
- Multiply both sides by -2:
- \(x = 0\)

2. For \(x - 20 = 0\):
- Add 20 to both sides:
- \(x = 20\)

Thus, the two horizontal distances when the height of the soccer ball equals 0 are \(x = 0\) (the start) and \(x = 20\) (when it hits the ground).

Therefore, the correct choice is:
**Solve the two equations: \(-\frac{1}{2}x = 0\) and \(x - 20 = 0\).**