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?(1 point)
Responses

15 feet
15 feet

30 feet
30 feet

−15
feet
negative 15 feet

7.5 feet
7.5 feet

Answer 1

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

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

We can rearrange this equation as follows:

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

Factoring out \(x\):

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

Setting each factor to zero gives us the potential solutions:

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

The solutions indicate that the firework reaches the ground at \(x = 0\) feet (the launch point) and \(x = 15\) feet (the point where it lands).

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

The correct response is:

**15 feet**.