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
15 feet

−15 feet
negative 15 feet

30 feet
30 feet

7.5 feet
7.5 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:

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

We can factor out \( x \):

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

Setting each factor equal to zero gives us:

1. \( x = 0 \)
2. \( -x + 15 = 0 \) which simplifies to \( x = 15 \).

The solutions to the equation are \( x = 0 \) and \( x = 15 \). The \( x = 0 \) solution indicates the starting point (when the firework is launched), and \( x = 15 \) represents the point where it will hit the ground.

Therefore, the firework will travel a distance of 15 feet before it reaches the ground.

Answer: 15 feet