Hi, Aerillious!

First let me fix your notation here, since HTML will by default eat extra spaces like that (put your stuff between [code] and [/code] tags to fix that, or better yet, learn to use ):

This does, more or less, use the standard method of completing the square. Let me try to elucidate it some more:

We have . First, when completing the square, you want to get rid of the coefficient of the 2nd-degree term. So they factored a -0.051 from the first two terms:

Now we take half of the coefficient of the linear term and square it.

Since our coefficient is , we find .

We can add and subtract this quantity like so:

But instead of leaving the second constant term inside the parentheses, let's move it outside, where it belongs, so that we can group it with the 1.6. To do this we must distribute the -0.051:

Now we factor the inner expression:

Note that , so we have

Looking at the standard form for the equation of a parabola with vertex at and focus at : , we see that our vertex is at .