Final answer:
The vertex of the parabola is (0,0), the focus is (0, -1/112), the directrix is y = 1/112, and the axis of symmetry is x = 0.
Step-by-step explanation:
The equation x = -1/28y^2 represents a parabola. To identify the vertex, focus, directrix, and axis of symmetry, we need to rewrite the equation in standard form, which is of the form (x-h)^2 = 4p(y-k), where (h,k) is the vertex and p is the distance between the vertex and the focus/directrix.
Comparing the given equation with the standard form, we can see that h = 0, k = 0, and p = -1/112. Therefore, the vertex is (0,0), the axis of symmetry is the vertical line x = 0, the focus is (0, -1/112), and the directrix is the horizontal line y = 1/112.