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

7.5 feet
7.5 feet

30 feet
30 feet

−15 feet

Answer 1

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

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

We can factor this equation:

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

Setting each factor to zero gives us:

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

The two solutions represent the points at which the firework is at ground level (height = 0). Since \( x = 0 \) is the launch point and we are looking for how far it will travel before reaching the ground again, we use the second solution:

The firework will travel 15 feet before it reaches the ground.

So the correct response is:

15 feet.