What real value of t produces the smallest value of the quadratic t^2 -12t - 36?
Hint: t^2 - 12t - 36 = (t - 6)^2 - 72. If you want t^2 - 12t - 36 to be the smallest, then you want (t - 6)^2 to be the smallest, but (t - 6)^2 is always >= 0. How can we make (t - 6)^2 = 0, so that the expression t^2 - 12t - 36 is minimized?
