In order to complete the square, the leading coefficient has to be a positive 1, which it is. Now we will set the polynomial equal to 0 and move the 2 over by subtraction to isolate the x terms. 
. The rule now is to take half the linear term, square it, and then add it in to both sides. Our linear term is 6. Half of 6 is 3, and 3 squared is 9, so we add 9 to both sides. 
. Simplifying we have 
. During this process, and the reason for it, was to create a perfect square binomial on the left which will give us the x coordinate (or the h) for our vertex. That perfect square binomial is 
. Now we will move the 7 over by subtraction and set the polynomial back equal to y to get 
. Our vertex, then, is (3, -7) and this is a min value since our parabola is positive and opens up like a cup that has a bottom instead of mountain that has a top. And there you go! Your answer is C