We can also complete the square. We can factor out a -1 from the given expression. We have -(t^2-8t+4). We can work inside the parenthesis. We can try to make the quadratic a perfect square. We have: t^2-8t+4=(t-4)^2-16+4=(t-4)^2-12. Remember the negative ;) We now have: -(t^2-4)^2+12. Since the negative of a positive number (a square) is always negative, the maximum it can be is 0. Therefore, the only possible maximum is 12. Hope this gives helpful insight :)
