1. What is Quadratic Regression?

Quadratic regression is a process of finding the equation of a parabola that best fits a set of data. It models relationships where the rate of change is not constant (curved relationships).

2. How Does the Calculator Work?

The calculator uses the quadratic equation:

Where:

• \( y \) — Dependent variable (output)
• \( x \) — Independent variable (input)
• \( a \) — Quadratic coefficient (determines curvature)
• \( b \) — Linear coefficient
• \( c \) — Constant term

Explanation: The equation describes a parabola where 'a' determines how steep or flat the curve is, 'b' affects the slope of the curve, and 'c' sets the y-intercept.

3. Importance of Quadratic Regression

Details: Quadratic regression is essential for modeling non-linear relationships in physics, economics, biology, and engineering where relationships aren't straight lines.

4. Using the Calculator

Tips: Enter the coefficients (a, b, c) and x value to calculate the corresponding y value on the parabola. All values can be positive or negative.

5. Frequently Asked Questions (FAQ)

Q1: When should I use quadratic regression?
A: When your data shows a curved pattern (U-shaped or inverted U-shaped) rather than a straight line relationship.

Q2: How is this different from linear regression?
A: Linear regression fits a straight line (degree 1 polynomial), while quadratic regression fits a parabola (degree 2 polynomial).

Q3: What does a negative 'a' coefficient mean?
A: A negative 'a' means the parabola opens downward (inverted U-shape), while positive 'a' means it opens upward (U-shape).

Q4: Can this calculate the vertex of the parabola?
A: This calculator solves for y given x. The vertex can be found at x = -b/(2a).

Q5: What are real-world applications?
A: Projectile motion, economic cost curves, biological growth patterns, and many other phenomena that follow curved relationships.