To determine the horizontal distance the ball has traveled when it hits the ground (i.e., when the height \( h(x) \) is equal to 0), Leon can use the Zero Product Property. This property states that if the product of two quantities is zero, then at least one of the quantities must be zero.
In the given equation:
\[ 0 = -\frac{1}{2} x (x - 20) \]
we can rewrite this as:
\[ -\frac{1}{2} x = 0 \quad \text{or} \quad x - 20 = 0 \]
Now, applying the Zero Product Property, Leon will set each factor equal to zero:
- From \(-\frac{1}{2} x = 0\), we find that \( x = 0 \).
- From \(x - 20 = 0\), we find that \( x = 20 \).
Thus, the horizontal distances at which the height of the soccer ball equals 0 are \( x = 0 \) (the initial point when the ball was kicked) and \( x = 20 \) (the point when it hits the ground).
Therefore, the correct response is:
Solve the two equations: − 1/2 x=0 and x−20=0.