Parabola Vertex Calculator

About this calculator

For a parabola written as y = ax² + bx + c, the vertex — the single point where the curve turns and reaches its maximum or minimum value — sits at x = −b ÷ (2a), with the corresponding y-value found by substituting that x back into the original equation. The vertical line through that x-value is the parabola’s axis of symmetry, splitting the curve into two mirror-image halves.

Algebra students use the vertex formula to graph parabolas quickly without plotting dozens of points, while the same math shows up in physics for finding the peak height and time of a projectile’s trajectory, and in business and economics for finding the maximum profit or minimum cost point of a quadratic revenue or cost model — anywhere a quantity is described by a quadratic function, its vertex marks the optimal point.

This calculator takes the coefficients a, b, and c of your parabola and returns the vertex coordinates and the equation of the axis of symmetry.