You can put this solution on YOUR website! Ok, this problem is easier than it looks because you get to reduce the craziness out of it. If: subtract y^2 from each side.
What that means is that you take a normal x^2 parabola, push it 2 to the left and up 3.
And parabolas only have 1 vertex. This one will be at the min, when the (x+2)^2 piece is 0. That's at x=-2. So vertex at (-2,3)