y^2=-2x Graph the equation. Identify the focus, directrix, and axis of symmetry of the parabola.

Let y^2=4px be equation of parabola. Then equation of directrix is x=-p coordinates of focus are (p,0) and axis of symmetry is x-axis.
In this case equation of parabola is
y^2=-2x
Therefore,
4p=-2
Divide by 4 to obtain p.
p=-2/4=-1/2
Using the facts stated above we can simply write the equation of directrix and coordinates of focus.
Directrix is the line x=1/2, focus is the point (-1/2,0) and the axis of symmetry is x-axis.                                   
https://en.wikipedia.org/wiki/Parabola