📉 Vertex of a Parabola Calculator
Enter the coefficients a, b, and c from a quadratic in the form y = ax² + bx + c to find its vertex.
What is the vertex of a parabola?
For a quadratic function y = ax² + bx + c, the graph is a parabola, and its vertex is the single point where the curve turns — the lowest point if the parabola opens upward, or the highest point if it opens downward.
The formula
The x-coordinate of the vertex is found with h = −b ÷ (2a), which is also the parabola’s axis of symmetry. Substituting h back into the original equation gives the y-coordinate, k = a·h² + b·h + c. When a is positive the parabola opens upward and k is a minimum value; when a is negative it opens downward and k is a maximum value.
This calculator also reports the discriminant (b² − 4ac), which tells you how many real roots the quadratic has, without needing a to be zero for a valid parabola.
This calculator is for general educational and reference purposes.