1. What is Completing The Square?

Completing the square is a method for converting a quadratic equation of the form ax² + bx + c into vertex form, which reveals the vertex of the parabola. This technique is useful for solving quadratic equations, graphing parabolas, and deriving the quadratic formula.

2. How Does the Calculator Work?

The calculator uses the completing the square formula:

Where:

• \( a \) — Coefficient of x² (must not be zero)
• \( b \) — Coefficient of x
• \( c \) — Constant term

Explanation: The process transforms the quadratic into vertex form, revealing the vertex at (-h, k) where h = b/(2a) and k = (b² - 4ac)/(4a).

3. Importance of Completing The Square

Details: Completing the square is essential for finding the vertex of a parabola, solving quadratic equations, deriving the quadratic formula, and understanding the properties of quadratic functions.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The coefficient 'a' must be non-zero. The calculator will display the equation in vertex form.

5. Frequently Asked Questions (FAQ)

Q1: Why complete the square instead of using the quadratic formula?
A: Completing the square gives the vertex form directly, which is useful for graphing and understanding the parabola's properties.

Q2: What if the coefficient 'a' is not 1?
A: The calculator handles any non-zero value of 'a' by factoring it out first.

Q3: How is this related to the quadratic formula?
A: The quadratic formula is derived by completing the square on the general quadratic equation.

Q4: Can this method solve all quadratic equations?
A: Yes, any quadratic equation can be solved by completing the square, though the quadratic formula may be more convenient.

Q5: What does the vertex form tell us?
A: The vertex form a(x - h)² + k shows the vertex at (h, k) and indicates whether the parabola opens up or down.