Quadratic Formula Calculator

Solve ax² + bx + c = 0 equations instantly

The quadratic formula calculator solves quadratic equations of the form ax² + bx + c = 0 using the quadratic formula. It provides real and complex roots, calculates the discriminant, shows step-by-step solutions, and even graphs the parabola. Perfect for students, teachers, and anyone needing to solve quadratic equations quickly.

Enter Coefficients:

x² +
x +
= 0

About the Quadratic Formula

The quadratic formula is used to find the roots of a quadratic equation of the form:

ax² + bx + c = 0

The formula is:

x = [ -b ± √(b² - 4ac) ] / 2a

Understanding the Discriminant

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

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

Practical Applications

Quadratic equations appear in many real-world situations including:

  • Physics (projectile motion)
  • Engineering (structural design)
  • Economics (profit maximization)
  • Computer graphics (curve rendering)
  • Architecture (parabolic designs)