Parabola Calculator

Parabola Calculator

Analyze the quadratic y = ax^2 + bx + c and extract the key geometric features.

Last updated: June 2026 | By Patchworkr Team

Quadratic coefficient set
Vertex
(2, -1)
opens upward
Focus
(2, -0.75)
Directrix
y = -1.25
Axis of symmetry
x = 2
y at x
-1
Roots
3, 1

Formula

y = ax^2 + bx + c

Vertex x = -b / (2a), focus is one focal length p = 1 / (4a) from the vertex, and the directrix is the same distance on the opposite side.

Related Tools