Completing the Square Calculator

Rewrite a quadratic ax² + bx + c in vertex form a(x − h)² + k by completing the square, and read off the vertex.

x2 + x +
Vertex form
h
k

How to Complete the Square

Enter the coefficients a, b and c.

1

Enter the coefficients

Type a, b and c from ax² + bx + c. a cannot be 0.

2

Read the vertex form

The quadratic is rewritten as a(x − h)² + k.

3

Read the vertex

The vertex of the parabola is the point (h, k).

Frequently Asked Questions

What does completing the square do?
It rewrites a quadratic ax² + bx + c as a(x − h)² + k, a form that makes the vertex and the graph easy to read off.
How do you find h and k?
The vertex x-coordinate is h = −b ⁄ (2a), and k = c − b² ⁄ (4a) is the value of the quadratic at that point.
What is vertex form used for?
Vertex form shows the parabola’s turning point directly, which helps with graphing, finding maxima or minima, and solving the equation.
Is my data sent anywhere?
No. Everything runs in your browser with JavaScript; nothing is uploaded or stored.