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)=−x^2+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=−x^2+15x. How far will the firework travel before it reaches the ground?(1 point)
Responses

30 feet
7.5 feet
−15
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 an x:

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

Setting each factor equal to zero gives us:

1. \( x = 0 \)
2. \( -x + 15 = 0 \) which simplifies to \( x = 15 \)

The two solutions indicate that the firework will be at ground level (height 0) at \( x = 0 \) feet (when it is shot) and at \( x = 15 \) feet when it comes back to the ground.

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

**The correct response is: 15 feet.**