Question 857859
You are missing something. There should be an equal sign somewhere.
Maybe you meant to type
(y + 2)^2 = -4(x-1) and got a + sign instead of the intended = sign.
 
{{{(y + 2)^2 = -4(x-1)}}}<-->{{{-(1/4)(y + 2)^2 = (x-1)}}}
is the equation of a parabola with a horizontal axis of symmetry,
{{{y+2=0}}}<-->{{{y=-2}}} ,
and the vertex at (1,-2).
The focal distance is {{{1}}} ,
and the focus and the rest of the parabola are to the left.
So the focus is at (0,-2),
{{{1}}} unit to the left of (1,-2),
and the directrix is the line {{{x=2}}} ,
{{{1}}} unit to the left of (1,-2).
{{{drawing(300,300,-5,5,-7,3,
graph(300,300,-5,5,-7,3,sqrt(4-4x)-2,-sqrt(4-4x)-2),
line(2,-7,2,3),circle(0,-2,0.1)
)}}}