Answer
$$\eqalign{
& {\text{Vertex }}\left( {0,0} \right) \cr
& \,\,\,\,\,\,\,{\text{Focus: }}\left( {p,0} \right):\,\,\left( { - \frac{1}{6},0} \right) \cr
& \,\,\,\,\,\,\,{\text{Directrix:}}\,\,x = - p:\,\,\,\,\,x = \frac{1}{6} \cr
& \,\,\,\,\,\,\,{\text{Horizontal axis of symmetry}} \cr
& \,\,\,\,\,\,\,{\text{Domain: }}\left( { - \infty ,0} \right] \cr
& \,\,\,\,\,\,\,{\text{Range:}}\left( { - \infty ,\infty } \right) \cr} $$
Work Step by Step
$$\eqalign{
& {y^2} = - \frac{2}{3}x \cr
& {\text{The equation is written in the form }}{y^2} = 4px \cr
& {y^2} = - \frac{2}{3}x \to \,\,\,\,\,\,\, - \frac{2}{3} = 4p\,\,\,\,\,\,\,\,p = - \frac{1}{6} \cr
& {\text{With: }} \cr
& \,\,\,\,\,\,\,{\text{Vertex }}\left( {0,0} \right) \cr
& \,\,\,\,\,\,\,{\text{Focus: }}\left( {p,0} \right):\,\,\left( { - \frac{1}{6},0} \right) \cr
& \,\,\,\,\,\,\,{\text{Directrix:}}\,\,x = - p:\,\,\,\,\,x = \frac{1}{6} \cr
& \,\,\,\,\,\,\,{\text{Horizontal axis of symmetry}} \cr
& \,\,\,\,\,\,\,{\text{Domain: }}\left( { - \infty ,0} \right] \cr
& \,\,\,\,\,\,\,{\text{Range:}}\left( { - \infty ,\infty } \right) \cr} $$
