Answer
Vertex: $(2,-1)$
Focus: $\left(1,-1\right)$
Directrix: $x=3$
See graph
Work Step by Step
We are given the parabola:
$(y+1)^2=-4(x-2)$
The standard equation is:
$(y-k)^2=4p(x-h)$
Determine $h,k,p$:
$h=2$
$k=-1$
$4p=-4\Rightarrow p=-1$
Determine the vertex:
$(h,k)=(2,-1)$
Determine the focus:
$(h+p,k)=\left(2+(-1),-1\right)=\left(1,-1\right)$
Determine the directrix:
$x=h-p$
$x=2-(-1)$
$x=3$
Determine the two points defining the latus rectum:
$x=1$
$(y+1)^2=4(-1)(1-2)$
$(y+1)^2=4$
$y+1=\pm 2$
$y+1=-2\Rightarrow y_1=-3$
$y+1=2\Rightarrow y_2=1$
$\Rightarrow (1,-3),(1,1)$
Plot the points, draw the directrix, and graph the parabola: