x+2=-2(y-3)2 has vertex at (-2,3) because, when y=3, x=-2, and x can have no higher value than -2 because x=-2(y-3)2-2, since -2(y-3)2 can never be positive. -2 is the maximum value for x, making (3,-2) the vertex.
This is a parabola lying on its side with arms extended to the left (negative). Therefore the axis of symmetry is horizontal. The focus and vertex lie on the axis of symmetry so have same y-coordinate, 3. The focus and directrix are equidistant from the vertex on the axis of symmetry. The leading coefficient of the squared term is -2 and, if f represents the focal distance, 1/(4f)=-2, so 4f=-½ and f=-⅛.
The focus lies inside the arms of the parabola so it's more negative than the vertex while the directrix line is more positive. Therefore, the focus is at (-2-⅛,3)=(-17/8,3) and the vertical directrix line is x=-2+⅛=-15/8.