About the Completing the Square Calculator
A clear, step-by-step path from standard form to vertex form.
What it is
The Completing the Square Calculator converts any quadratic axยฒ + bx + c into vertex form a(x โ h)ยฒ + k, showing the factoring, halving-and-squaring, and rewriting steps in order. It then derives the vertex, axis of symmetry, and roots โ the same technique used to derive the quadratic formula itself.
Features
Step-by-step derivation
Every algebraic move shown in order, not just the final vertex form.
Vertex, axis, roots
All three derived directly from the completed-square form.
Fractional precision
Clean fractions shown exactly instead of rounded decimals.
No-real-root handling
Complex-root cases explained clearly, never left as an error.