The height in feet of a projectile with an initial velocity of 32 feet per second and an initial height of 240 feet is a function of time in seconds given by

h(t) = −16t^2 + 32t + 240.

To find the height of the projectile at a specific time, we can use the given function h(t) = -16t^2 + 32t + 240.

Let's say we want to find the height at t = 3 seconds.
To do this, we substitute t = 3 into the function:

h(3) = -16(3)^2 + 32(3) + 240

First, simplify the equation inside parentheses:

h(3) = -16(9) + 32(3) + 240

Next, perform the multiplications:

h(3) = -144 + 96 + 240

Now, combine the like terms:

h(3) = 192

Therefore, the height of the projectile at t = 3 seconds is 192 feet.

To find the maximum height reached by the projectile, we need to determine the vertex of the parabolic function h(t) = -16t^2 + 32t + 240.

The vertex of a parabola in the form f(t) = at^2 + bt + c is given by the formula:
t = -b / (2a)

For our function h(t) = -16t^2 + 32t + 240, a = -16 and b = 32.

Substituting these values into the formula, we have:
t = -32 / (2 * -16)
t = -32 / -32
t = 1

The projectile reaches its maximum height at t = 1 second.

To find the maximum height, substitute this value of t back into the function h(t):
h(1) = -16(1)^2 + 32(1) + 240
h(1) = -16 + 32 + 240
h(1) = 256

Therefore, the maximum height reached by the projectile is 256 feet.