Write Quadratic Equation in Completed Square Form Calculator
Writing a quadratic equation in completed square form is a crucial step in solving quadratic equations. It’s the process of converting a quadratic equation into the form (x – h)^2 = k, where (h, k) is the vertex of the parabola represented by the equation.
How to Use This Calculator
- Enter the coefficients a, b, and c of your quadratic equation in the respective input fields.
- Click the “Calculate” button.
- View the completed square form of your equation and the corresponding graph in the results section.
Formula & Methodology
The formula to write a quadratic equation in completed square form is:
(x – (-b / (2a)))^2 = (4ac – b^2) / (4a)
This formula is derived from the quadratic formula x = [-b ± √(b^2 – 4ac)] / (2a), by completing the square.
Real-World Examples
Data & Statistics
| Equation | Completed Square Form |
|---|---|
| x^2 + 6x + 8 | (x + 3)^2 |
| x^2 – 4x + 3 | (x – 2)^2 |
Expert Tips
- Always check your answers by substituting the values back into the original equation.
- Practice makes perfect. The more you use this calculator and understand the process, the better you’ll get at writing quadratic equations in completed square form.
Interactive FAQ
What is the vertex of the parabola represented by a quadratic equation?
The vertex of the parabola is the point (h, k) where the parabola changes direction. It can be found using the formula (h, k) = (-b / (2a), 4ac – b^2) / (4a).
For more information, see the Math is Fun guide to quadratic equations.