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) = -x^2 + 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 = -x^2 + 15x.

How far will the firework travel before it reaches the ground?

A. 7.5 feet
B. 15 feet
C. 30 feet
D. -15 feet

Answer 1

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

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

We can start by factoring the equation. First, we can factor out \(x\) from the right side:

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

Setting each factor equal to zero gives us the possible solutions:

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

Thus, the firework will reach the ground at the points \(x = 0\) and \(x = 15\). The significant distance we are interested in (the non-zero distance where the firework lands) is:

\[
x = 15 \text{ feet}
\]

Therefore, the answer to how far the firework will travel before it reaches the ground is:

**B. 15 feet**