Amodel rocket is projected straight upward from the ground level according to the height equation h = -16t2 + 144t, t > 0, where h is the height in feet and t is the time in seconds. at what time is the height of the rocket maximum and what is that height?

This is a quadratic equation whose graph is a parabola that opens down.

When does the rocket reach its highest point?  Note that at that point it will stop ascending, momentarily stop, and then begin descending.   Note also that that point is the vertex of the parabola.

The easiest way to find that time value is to use the formula t = -b/(2a).

Here, t at max height is  t = -(144) / (2*[-16]) = 4.5 sec (answer.

What's the rocket's height there?  To answer this, sub 4.5 sec for t in the given equation, h(t) = -16t^2 + 144t.

Note:  Please use " ^ " to indicate exponentiation:  

 -16t^2 + 144t          (not     -16t2 + 144t)