Parabola Calculator — Vertex, Focus & Directrix
Use this free parabola calculator to analyze y = ax² + bx + c. It returns the vertex, focus, directrix, axis of symmetry, and vertex form, with a graph and step-by-step working.
Key features of a parabola
The vertex is at x = −b/(2a). The focal distance is p = 1/(4a): the focus sits p units from the vertex along the axis, and the directrix is the line p units on the other side.
Original price was: $109.99.$54.99Current price is: $54.99.
How to use it
- Enter a, b, and c.
- Press Analyze.
Related: the Completing the Square Calculator and more free math calculators.
Frequently asked questions
What are the focus and directrix?
Every point on a parabola is equidistant from the focus (a point) and the directrix (a line). They sit p = 1/(4a) units from the vertex.
Original price was: $109.99.$54.99Current price is: $54.99.
How do I get the vertex form?
The calculator rewrites y = ax²+bx+c as y = a(x−h)²+k where (h,k) is the vertex.
Original price was: $109.99.$54.99Current price is: $54.99.
Does it graph the parabola?
Yes, with the vertex, focus, and directrix marked.
Original price was: $27.99.$17.99Current price is: $17.99.
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