Parábola — Vértice
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
vértice (h, k)
About this calculator
This calculator finds the vertex coordinates of a parabola from the equation in vertex form y = a(x - h)² + k. The vertex is the point (h, k), representing the maximum or minimum of the quadratic function. You enter the values of a, h, and k, and the tool displays the vertex, concavity (upward if a > 0, downward if a < 0), and the maximum or minimum value.
The operation is simple: the calculator directly extracts the parameters h and k from the given equation. If the equation is in standard form y = ax² + bx + c, you must first convert it to vertex form by completing the square. The tool does not perform this conversion automatically; it assumes the input is already in (x - h)² form. Therefore, it is important that the user enters the correct values of h and k.
Use this calculator when you need to quickly determine the maximum or minimum point of a quadratic function, for example in optimization problems, physics (projectile motion), or economics (break-even point). It is also useful for checking results from analytic geometry exercises or for plotting the parabola graph accurately.
Caution: make sure the equation is in vertex form. A common mistake is confusing the sign of h: in y = a(x - h)² + k, the vertex is (h, k), not (-h, k). Also, if a = 0, the function is not quadratic and there is no parabola. The calculator does not handle incomplete equations or missing parameters.
Frequently asked questions
How do I convert the general equation y = ax² + bx + c to vertex form?
Complete the square: factor a from the x terms, add and subtract (b/2a)² inside the parentheses, and adjust the constant. The result will be y = a(x - h)² + k, where h = -b/(2a) and k = c - b²/(4a).
What does the value of 'a' in the equation mean?
The coefficient 'a' determines the concavity of the parabola. If a > 0, the parabola opens upward and the vertex is a minimum point. If a < 0, it opens downward and the vertex is a maximum point.
Can I use this calculator for equations with missing parameters?
No. The calculator expects numerical values for a, h, and k. If any parameter is missing, the tool will not work correctly. Make sure all fields are filled.
Does the calculator show the maximum or minimum value of the function?
Yes. It displays the value of k, which is the maximum (if a < 0) or minimum (if a > 0) value of the quadratic function.