Completing the square is a mathematical technique used to transform a quadratic equation into a perfect square trinomial. This method helps in solving equations, graphing parabolas, and finding the vertex of a quadratic function. The process involves rearranging the equation and adding a specific value to both sides to create a squared term. To complete the square, you take the coefficient of the linear term, divide it by two, square the result, and add it to both sides of the equation. This allows you to express the quadratic in the form of (x + p)^2 = q , making it easier to solve for x or analyze the graph of the function.