Parabolas

konartist

Find the vertex, focus, and the directrix of the parabola.

I get tripped up sometimes, but I know how to find all of the stuff with an equation like this :
(x+1)^2 +8(y+3) = 0

But how do I find it with equations like this
y^2=-6x

or

x+y^2=0

Can you complete the square with only two terms?

HallsofIvy

Reverse x and y! That is, change x+ y²= 0 to x²+ y= 0 which you know how to do. Once you have found the vertex, focus, directrix for that, switch back: If you found (a,b) as the vertex of x²+y= 0, then (b,a) is the vertex of x+ y²= 0. If you found y= c as the directrix of x²+ y= 0, then the directrix of
y²+ x= 0 is x= c.

konartist

My work

(x-h)^2=4p(y-k)
since h and k are 0 then the vertex = (0,0)
How do I find the focus and the directrix though?
Focus maybe = 4p = -6 P= -3/2 so the focus (0,-3/2) ?????
Directrix ?!?!?!?!?