During a water balloon fight, Louisa uses a slingshot to fire a water balloon over the fortified wall of the opponent. When fired from the slingshot, the balloon will follow the path h(x)=−x^2+12x

Question

, whereh(x)
is the height of the balloon in feet, and x is the horizontal distance it will travel. To determine how far the balloon will travel before it reaches the ground, Louisa sets the height equal to zero and solves the quadratic equation 0=−x^2+12x
. How far will the balloon travel before it reaches the ground?(1 point)
The balloon will travel
feet before it reaches the ground.

Answer 1

To find out how far the balloon will travel before it reaches the ground, we need to solve the equation \(0 = -x^2 + 12x\).

First, we can rearrange the equation:

\[ -x^2 + 12x = 0 \]

Factoring out \(x\):

\[ x(-x + 12) = 0 \]

This gives us two solutions:

1. \(x = 0\) (which is where it started)
2. \(-x + 12 = 0\) which simplifies to \(x = 12\)

Thus, the balloon will travel a total horizontal distance of 12 feet before it reaches the ground.