Solving Quadratic Equations Using Common Factors Quick Check

Question

3 of 53 of 5 Items
Question
As Isla prepares to set off fireworks, she wants to ensure the spectators are a safe distance away. When shot in the air, one firework will follow the pathh(x)=−x2+15x, where h(x) is the height of the firework, and x is the horizontal distance it travels in feet. To determine how far the firework will travel before it reaches the ground, Isla sets the height equal to zero, and solves the following quadratic equation: 0=−x2+15x. How far will the firework travel before it reaches the ground?(1 point)
Responses

7.5 feet
7.5 feet

−15 feet
negative 15 feet

30 feet
30 feet

15 feet
15 feet

Answer 1

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

\[ 0 = -x^2 + 15x \]

First, we can factor out a negative sign:

\[ 0 = -1(x^2 - 15x) \]

Next, we can factor the quadratic:

\[ 0 = -1(x(x - 15)) \]

Setting the factors equal to zero gives us:

\[ x = 0 \quad \text{or} \quad x - 15 = 0 \] \[ x = 0 \quad \text{or} \quad x = 15 \]

The firework reaches the ground when \( x = 15 \) feet.

Therefore, the firework will travel 15 feet before it reaches the ground.

The correct response is:

15 feet