Completing the Square Calculator
This calculator converts a quadratic expression ax² + bx + c into vertex form a(x + h)² + k. It displays the completed square form and identifies the vertex of the parabola.
Completing the square formula
Standard form: ax² + bx + c
Vertex form: a(x + h)² + k
Where: h = b/(2a), k = c - b²/(4a)
Vertex: (-h, k)
Completing the square: frequently asked questions
What is completing the square?
Completing the square is an algebraic method to rewrite a quadratic as a perfect square plus a constant: ax² + bx + c = a(x+h)² + k.
Why complete the square?
It helps find the vertex of a parabola, solve quadratic equations, and convert to vertex form for graphing.
How do I complete the square?
Divide by a, find (b/2a)², add and subtract it, factor the perfect square, and simplify.
What is vertex form?
Vertex form is a(x-h)² + k, where (h, k) is the vertex of the parabola. This form clearly shows the vertex and axis of symmetry.
Can I complete the square for any quadratic?
Yes, any quadratic expression can be rewritten in vertex form by completing the square.
Methodology
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026.