h(t)=4-16(t²-10t) is another way of writing the function.
h(t)=4-16(t²-10t+25-25) completes the square involving t.
h(t)=4-16((t-5)²-25) shows the square term which is always positive and has a minimum value of 0 when t=5. h(5)=4+16×25=404 feet is therefore the maximum height, because any value of t other than 5 will add a smaller number to 4.