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 travelfeet before it reaches the ground.

Answer 1

To find out how far Louisa's water balloon will travel before it hits the ground, we need to solve the equation:

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

We can rearrange this equation 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. \(x - 12 = 0 \Rightarrow x = 12\)

The solutions \(x = 0\) and \(x = 12\) represent the horizontal distances at which the height of the balloon is zero (i.e., it touches the ground). The balloon will travel a horizontal distance of 12 feet before it reaches the ground.

Therefore, the answer is:

The balloon will travel 12 feet before it reaches the ground.