1. What is Completing the Square?

Completing the square is a method for solving quadratic equations by converting them into perfect square trinomial form. This technique is fundamental in algebra and provides insights into the properties of quadratic functions.

2. How Does the Calculator Work?

The calculator uses the following process:

Where:

• \( h = -\frac{b}{2a} \)
• \( k = c - \frac{b^2}{4a} \)

Explanation: The calculator transforms the standard quadratic form into vertex form, revealing the vertex (h, k) of the parabola.

3. Importance of Completing the Square

Details: This method is essential for deriving the quadratic formula, graphing parabolas, solving optimization problems, and in calculus for integration techniques.

4. Using the Calculator

Tips: Enter coefficients a, b, and c from your quadratic equation ax² + bx + c = 0. Coefficient a cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: Why complete the square instead of using the quadratic formula?
A: Completing the square gives the vertex form which is useful for graphing and understanding the parabola's properties, not just the roots.

Q2: What if the discriminant is negative?
A: The calculator will show complex solutions in the form a ± bi.

Q3: Can I use this for equations where a ≠ 1?
A: Yes, the calculator handles all real values of a except zero.

Q4: How accurate are the results?
A: Results are rounded to 4 decimal places for readability while maintaining precision.

Q5: What applications does this have in real life?
A: Used in physics for projectile motion, engineering for optimization, economics for profit maximization, and more.