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?

Answer 1

To determine how far the balloon will travel before it reaches the ground, we need to solve the quadratic equation:
0=−x^2+12x

To solve this equation, we can factor it:
0 = -x(x - 12)

Setting each factor equal to zero, we have:
x = 0 or x - 12 = 0

Solving for x, we find:
x = 0 or x = 12

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