graph then find vertex & dirctrix of each parabola: x^2+2x-y+3=0

Recall that the parabola

x^2 = 4py has
vertex at (0,0)
directrix at y = -p
Your parabola is
(x+1)^2 = (y-2)
so, the vertex is at (-1,2)
the directrix is y-2 = -1/4