1. What is a Quadratic Equation?

A quadratic equation is a second-degree polynomial equation in a single variable x, with a coefficient a that is not equal to zero. The standard form is ax² + bx + c = 0 where a, b, and c are coefficients and constants.

2. How Does the Calculator Work?

The calculator uses the quadratic formula:

Where:

• \( a \) — Coefficient of x² (must not be zero)
• \( b \) — Coefficient of x
• \( c \) — Constant term

Explanation: The discriminant (b² - 4ac) determines the nature of the roots:

• Positive discriminant: Two distinct real roots
• Zero discriminant: Exactly one real root
• Negative discriminant: Two complex conjugate roots

3. Understanding the Solutions

Details: The solutions represent the x-intercepts (roots) of the parabola. The vertex form helps identify the maximum or minimum point of the parabola.

4. Using the Calculator

Tips: Enter the coefficients a, b, and c from your quadratic equation. The calculator will provide the roots and additional information about the parabola.

5. Frequently Asked Questions (FAQ)

Q1: What if a = 0?
A: If a = 0, the equation becomes linear (bx + c = 0) and has exactly one solution: x = -c/b.

Q2: What does the discriminant tell us?
A: The discriminant indicates the nature of the roots (real vs. complex) and how many times the parabola intersects the x-axis.

Q3: How is the vertex calculated?
A: The vertex is at x = -b/(2a), and you substitute this x-value into the equation to find the y-coordinate.

Q4: What does it mean if roots are complex?
A: Complex roots mean the parabola doesn't intersect the x-axis in real numbers, but the solutions exist in the complex plane.

Q5: Can this calculator handle very large/small numbers?
A: Within reasonable limits of floating-point arithmetic. Extremely large/small values may cause precision issues.