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

15 feet
15 feet

−15
feet
negative 15 feet

7.5 feet
7.5 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 the height function:

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

We can rearrange this equation:

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

Next, we can factor out \( x \):

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

Now we can set each factor equal to zero:

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

The solutions to the equation are \( x = 0 \) and \( x = 15 \). The solution \( x = 0 \) represents the position at launch, and \( x = 15 \) feet represents the horizontal distance traveled before the firework reaches the ground.

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

**Answer: 15 feet**