To find the horizontal distance the ball has traveled when the height is equal to 0 using the Zero Product Property, Leon should solve the equation:
\[ 0 = -12x(x - 20) \]
By the Zero Product Property, if the product of two factors is zero, at least one of the factors must be zero. Therefore, he can set each factor equal to zero:
- \(-12x = 0\)
- \(x - 20 = 0\)
Now, solving these equations:
-
For \(-12x = 0\): \[ x = 0 \]
-
For \(x - 20 = 0\): \[ x = 20 \]
Thus, the horizontal distances where the height is 0 are \(x = 0\) and \(x = 20\). This means the ball hits the ground at these two points (when it is kicked and when it lands).
Therefore, the correct response is:
Solve the two equations: −12x=0 and x−20=0.