1. What is Vertex Form?

The vertex form of a quadratic equation is an alternative way to express quadratic functions that makes identifying the vertex of the parabola straightforward. The general form is:

Where:

• \( a \) — Determines the parabola's width and direction (up/down)
• \( h \) — The x-coordinate of the vertex
• \( k \) — The y-coordinate of the vertex

2. How to Complete the Square

Step-by-Step:

1. Start with standard form: \( f(x) = ax^2 + bx + c \)
2. Factor out \( a \) from the first two terms
3. Add and subtract \( (b/(2a))^2 \) inside the parentheses
4. Simplify to vertex form

3. Importance of Vertex Form

Details: Vertex form immediately reveals the parabola's vertex (h,k), axis of symmetry (x=h), and whether it opens upward (a>0) or downward (a<0). This is crucial for graphing and solving optimization problems.

4. Using the Calculator

Tips: Enter coefficients a, b, and c from your quadratic equation in standard form (ax² + bx + c). The calculator will automatically complete the square and provide the vertex form.

5. Frequently Asked Questions (FAQ)

Q1: What if my 'a' coefficient is 0?
A: The equation wouldn't be quadratic. The calculator requires a ≠ 0.

Q2: How accurate are the results?
A: Results are accurate to 2 decimal places. For exact fractions, manual calculation may be needed.

Q3: Can I use this for complex numbers?
A: This calculator handles real numbers only.

Q4: What's the difference between vertex form and standard form?
A: Vertex form emphasizes the parabola's vertex and transformations, while standard form is better for finding y-intercepts.

Q5: How do I convert back to standard form?
A: Expand the squared term and combine like terms.