during a water balloon fight, Louisa uses a slingshot to fire a water balloon over the forfeited wall of the opponent fire 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 exes the horizontal distance. It will travel to determine how far the balloon will travel before it reaches the ground. Luisa says the highest equal to high equal to zero and solve the quadratic 0 = -X^2 +12 X how far will the balloon travel before I reached the ground
To determine how far the balloon will travel before it reaches the ground, we need to find the x-coordinates of the points where the height of the balloon is equal to zero.
The equation for the height of the balloon is H(x) = -x^2 + 12x. To find the x-coordinates where H(x) = 0, we set the equation equal to zero and solve for x:
0 = -x^2 + 12x
This is a quadratic equation in standard form. To solve it, we can factor out an x:
0 = x(-x + 12)
Setting each factor equal to zero gives us two possible solutions:
x = 0 or -x + 12 = 0
Solving the second equation for x gives:
x = 12
So the balloon will travel until it reaches the ground at x = 12 feet.