To determine how far the water balloon will travel before it reaches the ground, we need to solve the quadratic equation given by:
\[ 0 = -x^2 + 12x \]
We can rearrange this equation:
\[ -x^2 + 12x = 0 \]
Factoring out the common term \( x \):
\[ x(-x + 12) = 0 \]
This gives us two potential solutions:
- \( x = 0 \)
- \( -x + 12 = 0 \) which simplifies to \( x = 12 \)
The first solution, \( x = 0 \), represents the point where the balloon is released (initial position). The second solution, \( x = 12 \), represents the distance at which the balloon hits the ground.
Therefore, the balloon will travel 12 feet before it reaches the ground.