Free Online Calculator
Completing the Square Calculator
📐 Completing the Square Calculator
Convert quadratic equations to vertex form with step-by-step solutions
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📝 Detailed Solution Steps
Enter a quadratic equation in the Calculator tab to see detailed steps here.
📊 Parabola Graph and Vertex
Enter a quadratic equation to see its graph and vertex information.
🎓 Completing the Square Theory
Completing the square is a method to convert a quadratic equation from standard form to vertex form, revealing the vertex of the parabola.
Vertex Form: a(x - h)² + k = 0
Where: (h, k) is the vertex of the parabola
General Method:
Example: x² + 6x + 5
Applications:
- Finding Vertex: Identify the maximum or minimum point of a parabola
- Solving Quadratics: Alternative to quadratic formula
- Graphing: Easier to graph when in vertex form
- Optimization: Find maximum/minimum values in real-world problems
- Conic Sections: Standard form for parabolas in coordinate geometry
Key Formulas:
- Vertex x-coordinate: h = -b/(2a)
- Vertex y-coordinate: k = f(h) = ah² + bh + c
- Discriminant: Δ = b² - 4ac
- Axis of Symmetry: x = -b/(2a)
About This Calculator
Use the Completing the Square Calculator to solve polynomial or quadratic expressions from the entered coefficients and variables.
How We Keep This Calculator Reliable
SaralStudy calculators are built for learning, revision and planning with visible formulas and worked examples.
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