Question

Sam throws a rock up in the air. The equation h(t)=-16t^2+160t+4 represents the height of the rock in feet. What's the maximum height it reaches?

Answer 1

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.