You can put this solution on YOUR website!
So the height reached after 2 seconds is 192 ft.
To find maximum height we shall first express h(t) as a difference of two quantities the last one being a function of 't'.
Let's see this.
Now, h(t) is maximum when the second quantity i.e. that one on the right side of minus sign must be minimum.
is a perfect square and so cannot be negative.
So its minimum value is zero.
or t = 4
Hence h(t) is maximum when t = 4 seconds.
So maximum height reached is h(4) = 256 ft.
When the object will reach the ground, its height will be zero.
or t(8-t) = 0
So either t = 0 or 8 - t = 0 i.e. either t = 0 or t = 8
Now, at t = 0, the object was projected up.
So at t = 8 seconds the object must come down to ground.
Thus total time of flight is 8 seconds.
Note: This problem could also have been solved using Maxima & Minima principle of Calculus. But as the asker put it in quadratic section so I have solved this in this method.