Question

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)=−x2+12x
, 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=−x2+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 quadratic equation set by the height function:

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

First, let's rearrange the equation:

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

Now, we can factor out \(x\):

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

This gives us two potential solutions:

1. \(x = 0\)
2. \(-x + 12 = 0 \implies x = 12\)

The first solution, \(x = 0\), corresponds to the point when the balloon is initially fired (at the slingshot). The second solution, \(x = 12\), corresponds to when the balloon hits the ground.

Therefore, the balloon will travel **12 feet** before it reaches the ground.