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

−15 feet
negative 15 feet

30 feet
30 feet

15 feet
15 feet

7.5 feet
7.5 feet
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Answer 1

To find out how far the firework will travel before it reaches the ground, we set the height \( h(x) \) equal to zero and solve the equation:

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

First, we can rearrange the equation:

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

Next, we can factor out \( x \):

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

This gives us two possible solutions:

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

The value \( x = 0 \) corresponds to the launch point of the firework, and \( x = 15 \) corresponds to the point where the firework reaches the ground.

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

So, the correct response is:

**15 feet**