1. What is Quadratic Regression?

Quadratic regression is a process of finding the equation of a parabola that best fits a set of data. The quadratic equation has the form y = ax² + bx + c, where a, b, and c are coefficients that determine the shape and position of the parabola.

2. How Does the Calculator Work?

The calculator uses the quadratic equation formula:

Where:

• \( a \) — Quadratic coefficient (determines the curvature)
• \( b \) — Linear coefficient
• \( c \) — Constant term
• \( x \) — Input variable
• \( y \) — Output result

Explanation: The calculator takes the coefficients a, b, c and an x value, then computes the corresponding y value using the quadratic equation.

3. Applications of Quadratic Equations

Details: Quadratic equations are widely used in physics (projectile motion), engineering (structural design), economics (profit optimization), and computer graphics (curve rendering).

4. Using the Calculator

Tips: Enter the coefficients a, b, c and the x value you want to evaluate. The calculator will compute the corresponding y value using the quadratic formula.

5. Frequently Asked Questions (FAQ)

Q1: What does the coefficient 'a' represent?
A: The 'a' coefficient determines the curvature of the parabola. If a > 0, the parabola opens upward; if a < 0, it opens downward.

Q2: How do I find the vertex of the parabola?
A: The vertex can be found at x = -b/(2a), and then substitute this x value into the equation to find the y-coordinate.

Q3: What are the roots of a quadratic equation?
A: The roots (solutions) can be found using the quadratic formula: x = [-b ± √(b² - 4ac)] / (2a)

Q4: When does a quadratic equation have no real solutions?
A: When the discriminant (b² - 4ac) is negative, the equation has no real solutions, only complex ones.

Q5: Can this calculator solve for x given y?
A: No, this calculator solves for y given x. To solve for x given y, you would need to rearrange the equation and potentially use the quadratic formula.