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's represented by the equation y = ax² + bx + c, where a, b, and c are coefficients.

2. How Does the Calculator Work?

The calculator uses the quadratic regression equation:

Where:

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

3. Importance of Quadratic Regression

Details: Quadratic regression is used when data follows a parabolic trend. It's valuable in physics (projectile motion), economics (profit curves), biology (growth rates), and engineering.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation, along with the x value you want to evaluate. The calculator will compute the corresponding y value.

5. Frequently Asked Questions (FAQ)

Q1: How is this different from linear regression?
A: Quadratic regression fits a parabola (curved line) rather than a straight line, allowing for modeling of more complex relationships.

Q2: What does the coefficient 'a' represent?
A: The 'a' coefficient determines the parabola's width and whether it opens upward (a > 0) or downward (a < 0).

Q3: Can I use this for data analysis?
A: Yes, this calculator helps evaluate specific points on a quadratic curve, useful for predictions and analysis.

Q4: How accurate is quadratic regression?
A: It's highly accurate for data with a quadratic relationship. The R² value indicates goodness of fit.

Q5: What's the vertex form of this equation?
A: The vertex form is y = a(x - h)² + k, where (h,k) is the vertex. You can convert between forms.