Completing the Square

Completing the square is a method used to rewrite a quadratic equation in a form that makes it easier to find its roots or analyze its properties. It involves rearranging the equation so that one side becomes a perfect square trinomial—an expression like \((x + a)^2\). To do this, you adjust the constant term accordingly. This process reveals the vertex or minimum/maximum point of the parabola, helping to solve or graph the quadratic equation more intuitively. Essentially, completing the square transforms the equation into a pattern that isolates the squared term, simplifying analysis and solutions.