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
negative 15 feet

15 feet
15 feet

7.5 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 the height function, which is set to zero:

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

This can be rearranged into standard quadratic form:

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

Factoring out an \(x\):

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

Setting each factor equal to zero gives us:

1. \(x = 0\) (which represents the starting point of the firework),
2. \(-x + 15 = 0 \Rightarrow x = 15\) (the distance traveled before it hits the ground).

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

So, the correct response is:

**15 feet.**