Question

Find the vertex, focus and directrix. Then draw a graph.
( x+2) squared = -6( y-1)

Answer 1

this seems to be a good site http://www.scs.sk.ca/hch/harbidge/C30/Unit%201/2Parabola/2para.htm

Answer 2

to get the vertex get to the standard form (you're there already).
look at the bracketed terms
(x+2) - vertex is at x=-2
(y-1) = vertex is at y=1

Offset for the Focus (p) is found by dividing term in front of the y. 6 in this case by a factor of 4. so offet from vertex to focus is 1.5

Because y is expessed in terms of x^2 the parabola is vertical

6(y-1) = - (x+2)^2
6y = -1 x^2 - 4x -4 + 6
therefore because the term on the x^2 term is negative the parabola opens downwards

so the Focus point is (-2,1-1.5) = (-2, -0.5)

So what so we know
Vertex is at (-2,1)
Parabola is vertical and opens downwards
Focus is at (-2,-0.5)
Directrix is same distance 1.5 above the vertex that the focus is below it, so it is a line where y= 2.5

See the link above for how to sketch based on the info you now have