y=-½x² is the standard parabola form.
y=x²/4c where c is the distance between the vertex and the focus, which is inside the parabola. Therefore, 4c=-2, c=-½ and the vertex is at the origin.
The focus is at (0,-½). The directrix is outside the parabola the same distance from the vertex as the focus: y=½. The axis of symmetry is the y-axis (x=0).