Question 961582
{{{y=-(1/3)x^2}}}
or
{{{x^2=-3y}}}


Derive the formula for a parabola and compare.


The derivation uses directrix and focus.


Compare to {{{x^2=4py}}}.
{{{-3=4p}}}
{{{p=-3/4}}}
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The meaning for p is the distance from directrix or focus to the vertex.  The given parabola is inverted, so the vertex is a maximum point with vertical symmetry axis.  This one has vertex at the origin, (0,0), as seen from no add or subtract from x and no add or subtract from y.  The focus is (0,-3/4) and the directrix is y=3/4.