🧮 Completing the Square Calculator
Example equation: **x² – 6x + 8 = 0** → Enter **a=1, b=-6, c=8**
Result will appear here…
📌 What is Completing the Square?
Completing the square is a technique used in algebra to convert a quadratic equation into vertex form. This helps in solving equations, graphing parabolas, and finding roots more easily.
📌 Applications of Completing the Square
- Algebra: Solving quadratic equations.
- Graphing: Finding the vertex of a parabola.
- Physics: Used in projectile motion equations.
- Engineering: Helps in optimization problems.
📌 Example Calculations
| Quadratic Equation | Completed Square Form |
|---|---|
| x² – 6x + 8 = 0 | (x – 3)² – 1 = 0 |
| 2x² + 8x + 6 = 0 | 2(x + 2)² – 2 = 0 |
❓ FAQs
Q1: What is completing the square used for?
✅ It helps solve quadratic equations and find the vertex of a parabola.
Q2: Can completing the square be used for any quadratic equation?
✅ Yes, any quadratic equation can be rewritten in completed square form.
Q3: What if a ≠ 1 in the quadratic equation?
✅ Factor out ‘a’ before completing the square.
Q4: How does completing the square help in graphing?
✅ It shows the vertex, making it easier to sketch the parabola.
Q5: Is completing the square related to the quadratic formula?
✅ Yes! The quadratic formula is derived from completing the square.