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What is the minimum (extrema) of this equation?

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2 Answers

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;
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