To determine how far the water balloon will travel before it reaches the ground, we need to solve the equation for when the height \( h(x) \) is equal to zero. We start with the given equation:
\[ 0 = -x^2 + 12x \]
Rearranging it, we can write it as:
\[ -x^2 + 12x = 0 \]
Factoring out \( x \):
\[ x(-x + 12) = 0 \]
This gives us two solutions by setting each factor equal to zero:
- \( x = 0 \)
- \( -x + 12 = 0 \)
Solving the second equation for \( x \):
\[ -x + 12 = 0 \implies x = 12 \]
Thus, the two solutions are \( x = 0 \) and \( x = 12 \). The solution \( x = 0 \) corresponds to the moment the balloon is launched, and \( x = 12 \) is the horizontal distance at which the balloon hits the ground.
Therefore, the balloon will travel a distance of 12 feet before it reaches the ground.