Parabola Vertex Calculator

Summary

Enter a, b, c coefficients of ax² + bx + c to instantly find the vertex, axis of symmetry, focus, and directrix.

How it works

1. Enter the coefficient a (must be non-zero) for the x² term.
2. Enter coefficient b for the x term and c for the constant.
3. The vertex is computed as h = −b/(2a) and k = c − b²/(4a).
4. The axis of symmetry is the vertical line x = h.
5. The focus lies at (h, k + 1/(4a)) and the directrix is y = k − 1/(4a).
6. Copy any result with the copy buttons or read the formatted equation.

Use cases

• Check homework answers for parabola problems.
• Find the maximum or minimum point of a quadratic function.
• Determine the focal length for parabolic dish or antenna design.
• Verify graphing calculator results before an exam.
• Understand the relationship between vertex form and standard form.
• Quickly locate the directrix for conic section coursework.

Frequently Asked Questions