identify the vertex,focus,and directrix of the equation
y^2-4x-2y=3

identify the vertex,focus,and directrix of the equation
y^2-4x-2y=3


This web site tells a lot about parabolas:

Parabola - Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Parabola)

(x-h)^2=4p(y-k) (First equation)


axis parallel to the y-axis
vertex: (h,k)
focus: (h,k+p)
directrix: y=k-p



or

(y-k)^2=4p(x-h) (Second equation)


axis parallel to the x-axis
vertex: (h,k)
focus: (h,k+p)
directrix: y=k-p


Your equation is

y^2-4x-2y=3

y^2-2y=4x+3

The x's are now on the right, the y's on the left side. Let's concentrate on the left side. That's the most difficult since we have a square term. We note that

y^2-2y+1 = (y-1)^2 but we need a 1 on that side also. Add a 1 to both sides.

y^2-2y+1=4x+4

Now factor

(y-1)^2=4(x+1)

That looks like the second equation with k=1, p=1, h=-1.

You should be able to figure out the question now.