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.
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.
Frequently Asked Questions (FAQ)
What do I enter for a, b and c?
The coefficients of the quadratic equation ax squared plus bx plus c. For example, for x squared plus 6x plus 5, enter a=1, b=6 and c=5.
What steps does it show?
Each step appears in a separate row: divide, shift, complete the square and the vertex form.
Does it also show the roots?
Yes. Along with the steps and the vertex form, the tool gives the roots of the equation.
What is the vertex form used for?
The form a(x minus h) squared plus k shows the vertex (h, k) of the parabola, which makes sketching the graph easy.