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?
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.
To find out how far the balloon will travel before it reaches the ground, we need to solve the quadratic equation −x^2+12x = 0.
We can start by factoring out an x from the equation:
x(-x + 12) = 0.
Then, we set each factor equal to zero and solve for x:
x = 0
-x + 12 = 0.
For the first factor, x = 0, it means the balloon is at the starting point, which is not relevant for finding the distance it will travel before reaching the ground.
For the second factor, -x + 12 = 0, we add x to both sides of the equation to isolate x:
12 = x.
Therefore, the balloon will travel 12 feet before it reaches the ground.
To find how far the balloon will travel before it reaches the ground, we need to solve the quadratic equation:
0 = -x^2 + 12x
We can rearrange the equation to make it easier to solve:
x^2 - 12x = 0
Now, we can factor out an x:
x(x - 12) = 0
To solve this equation, we set each factor equal to zero:
x = 0 or x - 12 = 0
From the first factor, we get x = 0.
From the second factor, we get x - 12 = 0, which gives us x = 12.
Therefore, the balloon will travel 0 feet (at the starting point) and 12 feet (before it reaches the ground).