What is the minimum (extrema) of this equation?

Question

I need to know the extrema value for the following equation, preferably by solving it with completing the square.        f(x)=2x²-32x+74

Answer 1

Get the x value first using the axis of Symmetry -b/2a.  Once you get that x value just plug it in.  The answer you get will be the min

Answer 2

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.

 

x2-16x+37=x²-2*8*x+8²-8²+37=(x-8)²-64+37=(x-8)²-27.

 

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;