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 path h(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

30 feet
30 feet

15 feet
15 feet

7.5 feet
7.5 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 given by:

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

We can rearrange this equation:

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

Factoring out \( x \):

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

This gives us two factors:

1. \( x = 0 \)
2. \( -x + 15 = 0 \) → \( x = 15 \)

The solutions to the equation represent the points where the firework's height is 0 (i.e., when it reaches the ground). The two solutions \( x = 0 \) and \( x = 15 \) indicate that:

- \( x = 0 \) is the launch point of the firework.
- \( x = 15 \) is the point where the firework lands back on the ground.

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

The correct response is:

**15 feet**