Quadratic Formula Calculator

Understanding the Quadratic Formula

The quadratic formula is used to solve quadratic equations of the form ax² + bx + c = 0, where a, b, and c are coefficients and a ≠ 0. The formula gives the values of x that satisfy the equation:

How to Use the Quadratic Formula Calculator

1. Enter the coefficients a, b, and c from your quadratic equation ax² + bx + c = 0
2. Click the "Calculate" button
3. View the roots (solutions), discriminant, vertex, and other properties of the quadratic equation

Understanding the Results

Discriminant (b² - 4ac)

The discriminant tells you the nature of the roots:

• If discriminant > 0: Two distinct real roots
• If discriminant = 0: One real root (repeated)
• If discriminant < 0: Two complex conjugate roots

Vertex Form

The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex of the parabola. The vertex represents the minimum point (if a > 0) or maximum point (if a < 0) of the parabola.

Applications of Quadratic Equations

Quadratic equations are used in many real-world applications:

• Physics: Calculating projectile motion
• Engineering: Designing parabolic structures
• Economics: Modeling profit and revenue functions
• Computer graphics: Creating parabolic curves