How to Complete the Square
Step-by-step algebra for transforming quadratics into vertex form:
STEP 01
Factor Out a
Factor out coefficient a from x² and x terms: a(x² + (b/a)x) + c.
STEP 02
Take Half & Square
Calculate (b / 2a)² and add inside the parenthesis.
STEP 03
Balance Outside
Subtract a · (b / 2a)² on the outside to balance the expression.
STEP 04
Read Vertex
Form is a(x - h)² + k with vertex (h, k).