Completing the Square Calculator

Unlock the vertex form of quadratic equations and visualize parabolas effortlessly.

Coefficient of x² (a):

Coefficient of x (b):

Constant term (c):

Completed Square Form:

Quadratic Function Visualization

Understanding Completing the Square

Completing the square is a technique used to rewrite a quadratic expression in vertex form, which is $a(x-h) 2 + k$ . This form reveals the vertex of the parabola at point $(h, k)$ , making it easier to analyze and graph quadratic functions.

This method is valuable for solving quadratic equations, understanding the properties of parabolas, and in calculus. By transforming a quadratic to vertex form, we gain direct insight into the parabola's vertex and axis of symmetry.

For example, consider $x 2 + 6x + 5$ . Completing the square gives $(x+3) 2 - 4$ , revealing the vertex at $(-3, -4)$ .