Parabola Vertex Calculator

Summary

This calculator finds all key properties of a parabola defined by f(x) = ax² + bx + c. Enter the three coefficients and get the vertex coordinates, axis of symmetry equation, focus point, directrix line, and whether the parabola opens up or down. All calculations are instant and computed in your browser.

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