Math

Completing the Square Calculator

Convert ax² + bx + c into vertex form a(x − h)² + k. Get the vertex, axis of symmetry, and step-by-step working in seconds.

Vertex Form Vertex (h, k) Axis of Symmetry Step-by-step

Quadratic to Vertex Form

Enter a, b, c for y = ax² + bx + c. Choose decimals or fractions, then generate the completed-square form and steps.

a (x² coefficient)

b (x coefficient)

c (constant)

Output Format

Decimal Precision

Number Formatting

Tip: If you’re graphing, vertex form instantly shows the vertex and whether the parabola opens up (a > 0) or down (a < 0).

Steps are shown in a clean algebra flow: factor out a, create a perfect square trinomial, then simplify into a(x − h)² + k.

Goal	What you need	Why completing the square helps
Find the vertex	(h, k)	Vertex form shows the vertex directly
Graph fast	Shape + center	a controls opening; h shifts left/right; k shifts up/down
Solve ax² + bx + c = 0	Roots	Rewrite to a(x − h)² = −k, then take square roots
Optimization	Min/Max value	k is minimum (a>0) or maximum (a<0)

Use “Fractions” output if your teacher expects exact values like h = 3/2 instead of 1.5.