`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.              ...

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.