Complex domain and range word problem

[Sean O'Connor]

Here's the problem I'm having trouble with: An object was shot up into the air at an initial vertical speed of 384 feet per second. Its height as time passes can be modeled by the quadratic function f, where f(t)= -16t^2 +384t. Here t represents the number of seconds since the objects release, and f(t) represents the objects height in feet

The function's domain in this context is:

The function's range in this context is:

 

[tkhunny]

How long does it stay up? (Time in the air. The definition of t)
How high does it go? (All distances actually obtained during flight. The definition of F(t))

 

[Steven G]

It should state more clearly that f(t) is the height the object is above the ground (so f is 0 when the object hits the ground).
The object covers the range from a height of 0 all the way to its highest point. The domain is the time the object is in the air (who would keep the timer going after the ball hits the ground!) I hope that it is clear that the time starts at t=0 when the object is launched and ends when the object hits the ground.

What you need to do is just turn this problem into a parabola problem. max height = vertex of the parabola. What does the x-intercept mean in this problem. Draw the exact parabola and post it here. That will be the best way to help you.