Find the vertex, focus, directrix and axis of symmetry of a parabola y=ax²+bx+c.
A parabola y = ax² + bx + c has its vertex at x = −b/(2a). The focus lies 1/(4|a|) units from the vertex along the axis of symmetry, and the directrix is the same distance on the opposite side.
Vertex
x_v = −b/(2a), y_v = f(x_v)
Focal Distance
f = 1/(4|a|)
If a > 0 the parabola opens upward; if a < 0 it opens downward.
It is the vertical line x = −b/(2a), passing through the vertex.