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)=−x^2+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=−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:

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

We can factor this equation:

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

Setting each factor equal to zero gives us:

1. \( x = 0 \) (This represents the initial position when the balloon is fired.)
2. \( -x + 12 = 0 \) which simplifies to \( x = 12 \).

Thus, the balloon will reach the ground when \( x = 12 \) feet.

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