as Isla prepares to set up fireworks, she wants to ensure the spectators are safe distance away when the air on firework will follow the path h(x) = -x^2 + 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 is the height equal to zero, and solve the following quadratic equation: 0 = -x^2 + 15x. How far will the firework travel before it reaches the ground
To determine the distance the firework will travel before it reaches the ground, we need to solve the quadratic equation:
0 = -x^2 + 15x
To solve this equation, we can set it equal to zero and factor it:
0 = x(x - 15)
Now we have two solutions:
x = 0
x - 15 = 0
The first solution, x = 0, means that the firework started at the ground. However, this solution does not give us any meaningful distance traveled before reaching the ground.
The second solution, x - 15 = 0, gives us x = 15. This means that the firework will travel 15 feet before it reaches the ground.