1. What is Vertex Form?

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) represents the vertex of the parabola. This form clearly shows the vertex and the direction/width of the parabola.

2. How Does the Conversion Work?

The conversion from standard form (y = ax² + bx + c) to vertex form involves completing the square:

Where:

• \( a \) — Coefficient of x²
• \( b \) — Coefficient of x
• \( c \) — Constant term
• \( h \) — x-coordinate of vertex
• \( k \) — y-coordinate of vertex

Explanation: The vertex form makes it easy to identify the parabola's vertex and axis of symmetry.

3. Importance of Vertex Form

Details: Vertex form is particularly useful for graphing quadratic functions and solving optimization problems, as it directly shows the maximum or minimum point of the parabola.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your standard form quadratic equation (y = ax² + bx + c). The calculator will provide the equivalent vertex form.

5. Frequently Asked Questions (FAQ)

Q1: What if a = 0?
A: If a = 0, it's not a quadratic equation (it becomes linear). The calculator requires a ≠ 0.

Q2: How accurate are the results?
A: Results are rounded to 2 decimal places for readability, but calculations use full precision.

Q3: Can I use fractions?
A: The calculator accepts decimal numbers. For fractions, convert them to decimals first.

Q4: What does the vertex represent?
A: The vertex is the parabola's maximum or minimum point, depending on whether a is negative or positive.

Q5: Can this calculator work backwards?
A: Currently it only converts from standard to vertex form. Future versions may include reverse conversion.