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

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)
Responses

30 feet
30 feet

15 feet
15 feet

−15 feet
negative 15 feet

7.5 feet
7.5 feet

GPT-4o mini · Answer

To determine 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:

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

Factoring out \(x\):

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

This gives us two possible solutions:

\( x = 0 \) (the initial launch position),
\( -x + 15 = 0 \) which simplifies to \( x = 15 \).

Thus, the firework will reach the ground after traveling 15 feet.

So the correct response is 15 feet.