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 fits a quadratic equation of the form y = ax² + bx + c to the observed data.

2. How Does the Calculator Work?

The calculator uses the quadratic equation:

Where:

• \( a \) — Quadratic coefficient (determines parabola's width and direction)
• \( b \) — Linear coefficient
• \( c \) — Constant term (y-intercept)
• \( x \) — Independent variable input
• \( y \) — Dependent variable output

Explanation: For any given x value, the calculator computes the corresponding y value on the quadratic curve defined by coefficients a, b, and c.

3. Importance of Quadratic Regression

Details: Quadratic regression is used when the relationship between variables follows a parabolic pattern. It's widely used in physics, engineering, economics, and biological sciences to model non-linear relationships.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c that define your quadratic equation, then enter the x value for which you want to calculate y. All values can be positive or negative decimals.

5. Frequently Asked Questions (FAQ)

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

Q2: How is this different from linear regression?
A: Quadratic regression can model curved relationships while linear regression only models straight-line relationships.

Q3: What does a negative 'a' coefficient mean?
A: A negative 'a' means the parabola opens downward, while positive 'a' means it opens upward.

Q4: Can I use this for extrapolation?
A: Be cautious with extrapolation as quadratic functions can diverge rapidly outside the range of observed data.

Q5: How do I find the vertex of the parabola?
A: The vertex x-coordinate is at x = -b/(2a), then plug this x back into the equation to find y.