I need to know the extrema value for the following equation, preferably by solving it with completing the square. f(x)=2x2-32x+74
First, 2 can be factored out, it does not change the extrema positions.
2*(x2-16x+37); Let us from now operate on the trinomial inside the parentheses.
This expression has a minimum when (x-8)2 is minimal. Since square of any number is nonnegative, the minimum is attained when (x-8)2=0 or x=8. In this case f(8)=-27;