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)

Question

Responses

−15 feet
negative 15 feet

15 feet
15 feet

7.5 feet
7.5 feet

30 feet
30 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:

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

We can rearrange the equation as follows:

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

Factoring out \( x \):

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

This gives us two possible solutions:

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

The second solution means that the firework will hit the ground 15 feet away from the launch point.

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

The correct response is:

15 feet