Recall that the given function is a parabola. It looks something like this
The highest point of this parabola is the vertex. recall that the general equation of a parabola is of the form

where h and k are the coordinates of the vertex. We are interested at the coordinate h. So what we will do is complete the square to get the general equation. So we start with

we factor out -16, so we get

Now, note that

So this implies that

so we replace this value and we get

note that in this expression, the value of h would be 3/2. So the time it needs to reach its maximum height is 3/2 seconds. The highest point would be the value of k. So, in this case we have

so the highest point is would be 36 meters.