Solving Quadratic Equations Using Common Factors Practice

Question

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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)=−x2+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=−x2+12x
. How far will the balloon travel before it reaches the ground?(1 point)
The balloon will travel
feet before it reaches the ground.
Remaining Attempts : 3

Answer 1

To determine how far the balloon will travel before it reaches the ground, we need to solve the quadratic equation:

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

First, we can factor the equation:

1. Rearranging gives us: \[ -x^2 + 12x = 0 \]

2. Factoring out a common factor of \( x \): \[ x(-x + 12) = 0 \]

3. Setting each factor to zero gives: \[ x = 0 \] \[ -x + 12 = 0 \Rightarrow x = 12 \]

So, the solutions to the equation are \( x = 0 \) and \( x = 12 \).

Since \( x = 0 \) corresponds to the moment the balloon is released from the slingshot, the balloon will reach the ground when \( x = 12 \).

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