Question

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

7.5 feet
7.5 feet

15 feet
15 feet

−15
feet
negative 15 feet

30 feet

Answer 1

To determine how far the firework will travel before it reaches the ground, we need to solve the equation \( 0 = -x^2 + 15x \).

First, let's rearrange the equation:

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

Factoring out \( x \):

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

Setting each factor equal to zero gives us:

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

The solutions \( x = 0 \) and \( x = 15 \) indicate that the firework will be at ground level (height = 0) at these two points.

Since \( x = 0 \) represents the starting point of the firework, the distance it travels before it reaches the ground is:

\[ \boxed{15 \text{ feet}} \]