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

Question

, 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 travels before it reaches the ground, we need to solve the equation

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

We can factor out the equation:

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

Setting each factor equal to zero gives us:

1. \( -x = 0 \) ⇒ \( x = 0 \)
2. \( x - 12 = 0 \) ⇒ \( x = 12 \)

The two solutions are \( x = 0 \) and \( x = 12 \). The value \( x = 0 \) corresponds to the point where the balloon is launched, and \( x = 12 \) is where it hits the ground.

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