Consider the parabola (y + 1) 2 = 2 (x + 1). Which equation is used to find the directrix?

For finding the directrix you don't need any equations.

(y-b) ^2=4p (x-a)

this is a Horizontal parabola.

the distance between directrix and vortex is p

p is 1/2 and vortex is (-1,-1) so directrix passes from - 1/2.

x=-1/2