For this, I got the equation (X+3)^2-2 or X^2+6X+7. I used this method:
First I set up an equation (X+H)^2-K, where (K, H) is the vertex. All we have to do is find where the graph reaches its minimum value (because it opens upwards), then find the x-coordinate that lies there, which is (-2,3). Substituting these value in for H and K, we get the equation (X+3)^2-2 or simplified X^2+6X+7.
:)