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

Question

h
(
x
)
=
−
x
2
+
15
x
, 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
0
=
−
x
2
+
15
x
. How far will the firework travel before it reaches the ground?(1 point)
Responses

−15
−
15
feet
negative 15 feet

7.5 feet
7.5 feet

15 feet
15 feet

30 feet

Answer 1

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

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

We can rearrange this equation to:

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

Factoring out \( x \):

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

This gives us two solutions:

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

The solutions indicate that the firework will be at ground level at \( x = 0 \) feet (the starting point) and again at \( x = 15 \) feet.

Thus, the firework will travel a distance of 15 feet before it reaches the ground.

The correct response is:

15 feet