Completing the Square Calculator
Enter the coefficients a, b and c of a quadratic equation and watch every completing-the-square step — dividing, shifting, square completion and vertex form — with roots given too, ideal for students checking homework or learning the method.
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How to use
- Enter a, b and c of the quadratic ax^2 + bx + c.
- Each step will show in a separate row — divide, shift, complete the square, vertex form.
- Roots are also given as a cross-check with the quadratic formula.
Note: Vertex form is a(x - h)^2 + k where h = -b/(2a) and k = c - b^2/(4a). This form is used to find the vertex of the parabola and to sketch the graph.
Tips
- Always divide through by a first so the x-squared coefficient becomes 1.
- The number you add and subtract is (b/2a) squared — that is what completes the square.
- Vertex form a(x - h) squared + k gives the vertex (h, k) of the parabola directly.
- Use the roots line to cross-check your hand-written working.