Question 723666
The standard equation for a parabola with its axis vertical is:

{{{(x -h)^2 = 4a(y-k)}}} ...(1)

The vertex is ({{{h}}},{{{ k}}}).
The focus is ({{{h}}},{{{ k + a}}}).
The directrix is {{{y = k -a}}}.

you have

{{{y = (1/12)x^2 }}}...solve for {{{x^2}}}

{{{y /(1/12)= x^2 }}}

{{{12y = x^2}}} ....write it in form given above

{{{12(y-0) = (x-0)^2 }}}

as you can see

{{{h=0}}}
{{{k=0}}}
{{{4a=12}}}...=>...{{{a=3}}}

than,
the vertex is ({{{h}}},{{{ k}}})=({{{0}}},{{{0}}})
the focus is ({{{h}}}, {{{k + a}}})= ({{{0}}}, {{{0 + 3}}})=({{{0}}},{{{ 3}}})
the directrix is {{{y = k -a}}}...=>..{{{y = 0-3}}}...=>..{{{y =-3}}}

so, your answer is: 

focus: ({{{0}}},{{{ 3}}}) ; directrix: {{{y =-3}}}


{{{drawing ( 600, 600, -5, 5, -5,5, circle(0,3,.1),graph( 600, 600, -5, 5, -5, 5, (1/12)x^2,-3)) }}}