SOLUTION: I have to find the coordinates of the focus, vertex, axis of symmetry, and directrix. x=1/4y^2-1/2y-3 I got stuck after I factored out the 1/4. Thank you in advance!

The easiest way when there are fractions is to clear of fractions
first.  Multiply through by 4




Add 12 to both sides



Complete the square on the right:

Multiply the coefficient of y by :  = -1
Square that result 
Add +1 to both sides



Factor the right side:

       



Factor 4 out of the left sides:



Multiply both sides by 



Compare to 



and we have vertex = (h,k) = (,1), 4p=, p=

It is a parabola with horizontal axis of symmetry, the green line below
whose equation is y=1, since 1 is the y-coordinate of the vertex.



To find the focus we know it is p= of a unit right of the vertex,
so we add  to the x-coordinate of the vertex:

 and the y-coordinate of the focus is
the same as the y-coordinate of the vertex, or 1.

So the focus is the point (,1)

The directrix is a blue line p= of a unit left of the vertex.


So the equation of the directrix is 

The focus is the point (,1) marked just right of the vertex 
and the directrix is the blue line :



Edwin