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

30 feet
30 feet

15 feet

Answer 1

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

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

This can be rearranged to:

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

Factoring out \(x\):

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

Setting each factor equal to zero gives us:

1. \( x = 0 \) (the initial point where the firework is launched)
2. \( x - 15 = 0 \) which leads to \( x = 15 \)

Therefore, the firework will reach the ground again when \(x = 15\) feet.

The answer is: 15 feet.