What is the purpose of completing the square?

• A. To rewrite the expression as a product of linear factors
• B. To identify the vertex directly
• C. To convert the quadratic expression into a perfect square trinomial
• D. To solve by substitution

Answer: (C)

Completing the square is a technique used to rewrite a quadratic as a perfect square trinomial plus or minus a constant. This changes the expression into the form (x + p)^2 + q, which makes the square structure visible.

Why that form matters: it directly shows the vertex of the parabola, since the vertex is at (-p, q). It also makes solving or graphing easier, because you can take square roots or read off key features from the square form.

So the main purpose is to convert the quadratic into a perfect square trinomial (and then into a squared binomial), which then reveals the vertex and aids solving and graphing.