Completing the Square Calculator
How It Works
This completing the square calculator uses established formulas to provide accurate results.
The basic rule:
- a(x - h)² + k where h = -b/(2a) and k = c - b²/(4a)
- Step 1: Factor out a from first two terms
- Step 2: Add and subtract (b/2a)² inside
- Step 3: Simplify to vertex form
Results are estimates. Consult a professional for critical decisions.
Want to Actually Learn Algebra?
Calculators give you answers — but if you want to understand the math, Allday Everyday Math teaches Algebra 1 fast with structured lessons, worked examples, and practice quizzes that build real confidence.
Explore Allday Everyday Math →Frequently Asked Questions
What is completing the square?
Completing the square is a technique that rewrites ax² + bx + c as a(x - h)² + k. This reveals the vertex of the parabola and makes it easy to solve the equation or graph it.
Why is vertex form useful?
Vertex form a(x-h)²+k immediately tells you the vertex (h,k), the axis of symmetry (x=h), and whether the parabola opens up (a>0) or down (a<0). It also makes graphing much easier.
How do you complete the square step by step?
1) If a≠1, factor it out from the x terms. 2) Take half the coefficient of x and square it. 3) Add and subtract that value inside the parentheses. 4) Factor the perfect square trinomial and simplify.