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(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 solve 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 7.5 feet 7.5 feet 15 feet 15 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 rearrange this equation as follows:

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

Factoring out \( x \):

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

Setting each factor to zero gives us:

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

These values represent the points when the firework is at a height of zero (when it first launches at the ground and when it lands back on the ground).

Thus, the firework will travel \( 15 \) feet horizontally before it reaches the ground.

The correct response is 15 feet.