Question 981055
{{{(-1/3)y=(x+1/2)^2}}}

Compare this to {{{4py=(x-h)^2}}}.


Yours has {{{4p=-1/3}}}
{{{p=-1/12}}}.


The directrix is  {{{1/12}}} units away from the vertex and is on the convex side of the vertex (0,-1/2).  Focus is {{{1/12}}} units below the vertex.  The parabola is vertical and opens downward.


Focus:  {{{y=-1/2-1/12=-6/12-1/12=-7/12}}}, or  (0, -7/12).
Directrix:  The line {{{y=-1/2+1/12=-5/12}}} or {{{y=-5/12}}}.
Vertex:  ( 0,-1/2).


Refer in your book to the derivation of a parabola equation for horizontal directrix with focus on the x-axis; and that p is the distance from either focus or directrix.


{{{graph(250,250,-3,3,-3,3,-3(x+1/2)^2)}}}