1. What is Standard Form to Vertex Form Conversion?

The process of converting a quadratic equation from standard form (ax² + bx + c) to vertex form (a(x - h)² + k) is called completing the square. This form reveals the vertex of the parabola directly as (h, k).

2. How Does the Calculator Work?

The calculator uses the completing the square method:

Where:

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

Explanation: The calculator finds the vertex (h, k) and rewrites the equation in vertex form.

3. Importance of Vertex Form

Details: Vertex form immediately shows the parabola's vertex, axis of symmetry, and whether it opens upward or downward. This is crucial for graphing and analyzing quadratic functions.

4. Using the Calculator

Tips: Enter coefficients a, b, and c from your quadratic equation in standard form. Coefficient a cannot be zero (must be quadratic).

5. Frequently Asked Questions (FAQ)

Q1: Why convert to vertex form?
A: Vertex form makes it easy to identify the vertex, axis of symmetry, and maximum/minimum values of the quadratic function.

Q2: What if a = 0?
A: If a = 0, the equation is linear, not quadratic. The calculator requires a quadratic equation (a ≠ 0).

Q3: How accurate are the results?
A: Results are rounded to 2 decimal places for clarity. For exact fractions, manual calculation may be needed.

Q4: Can this calculator handle complex numbers?
A: No, this calculator only works with real number coefficients and real roots.

Q5: What's the difference between standard and vertex form?
A: Standard form shows y-intercept clearly, while vertex form shows the vertex and transformations of the basic parabola.