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
, where h(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 determine how far the water balloon will travel before it reaches the ground, we need to solve the equation:

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

We can rearrange this equation into standard quadratic form:

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

This is equivalent to:

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

Next, we can factor the equation:

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

Setting each factor equal to zero gives us:

1. \( x = 0 \)
2. \( -x + 12 = 0 \) or equivalently, \( x = 12 \)

The solutions represent the points where the balloon is at ground level. The values signify:

- \( x = 0 \): the starting point of the balloon (when it was fired)
- \( x = 12 \): the point where the balloon hits the ground

Thus, the distance that the balloon travels before it reaches the ground is \( 12 \) feet.

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