Answer
$$\eqalign{
& {\text{focus: }}\left( { - 1,0} \right) \cr
& {\text{directrix: }}x = 1 \cr
& {\text{axis of symmetry: }}y = 0 \cr} $$
Work Step by Step
$$\eqalign{
& {y^2} = - 4x \cr
& {\text{This equation is written in the form }}{y^2} = 4px.{\text{ }} \cr
& {\text{represents a parabola with Horizontal Axis }} \cr
& {\text{of Symmetry and Vertex }}\left( {0,0} \right). \cr
& \underbrace {{y^2} = - 4x}_{{y^2} = 4px} \cr
& - 4x = 4px \cr
& p = - 1 \cr
& {\text{With focus}}\left( {p,0} \right){\text{ and directrix }}x = - p \cr
& {\text{focus: }}\left( { - 1,0} \right) \cr
& {\text{directrix: }}x = 1 \cr
& {\text{axis of symmetry: }}y = 0 \cr} $$
