As isla prepares to set off fireworks she wants to ensure the spectators are a safe distance away when shot in the air one fireworks will follow the path h (x) =!-x^2 + 15x where h (x) is the height of the firework and 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 = -x^2 + 15x how far will the firework travel before it reaches the ground?

Question

A. 15 feet
B. -15 feet
C. 7.5 feet
D. 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 \( h(x) = -x^2 + 15x \) by setting it equal to zero:

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

We can factor the equation:

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

This gives us two solutions:

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

The solutions indicate that the firework reaches the ground (height = 0) at \( x = 0 \) (the starting point) and at \( x = 15 \).

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

The correct answer is A. 15 feet.