Answer:
The function given here is a quadratic function of the form f(t) = at^2 + bt + c, where a is -2, b is 8, and c is 300. The maximum value of a quadratic function occurs at its vertex. For a function in the form f(t) = at^2 + bt + c, the t-coordinate of the vertex is given by -b/(2a). We can use this to find the time at which the firework reaches its maximum height.
Given a = -2 and b = 8, we can calculate t = -b/(2a):
t = -8/(2*-2) = 2
We can then substitute this value back into the height equation to find the maximum height:
h(2) = -2(2)^2 + 8*2 + 300
h(2) = -8 + 16 + 300
h(2) = 308
So, the greatest height the fireworks reach is 308 feet.