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It's a method called "completing the square". We add/subtract an appropriate constant term that allows us to condense three terms into a squared binomial, and leaves a constant remainder outside the squared term.

In this case, we first factor out -16 from the first two terms:

When we square a binomial like , we end up with the expansion , so that in the quadratic above we need with and . Then the constant term we have to add/subtract will be :

Now the first three terms within the parentheses can be condensed to get

and all that's left to do is distribute a factor of -16 and combine the remaining constant term:

Then the vertex of the parabola defined by this expression occurs at .