Quadratic Formula Calculator
Solve ax² + bx + c = 0 using the quadratic formula. Find real and complex roots, discriminant, vertex, and graph properties.
ax² + bx + c = 0
Related Calculators
You might also find these calculators useful
Quadratic Equation Solver
Solve any quadratic equation instantly using the quadratic formula. Enter coefficients a, b, and c to find roots (real or complex), the discriminant, vertex coordinates, and axis of symmetry. Perfect for algebra, physics, and engineering.
The Quadratic Formula
The quadratic formula x = (-b ± √(b²-4ac)) / 2a solves equations of the form ax² + bx + c = 0. The discriminant (b²-4ac) determines the nature of roots: positive gives two real roots, zero gives one repeated root, negative gives two complex conjugate roots.
Quadratic Formula
x = (-b ± √(b²-4ac)) / 2aHow to Use This Calculator
Quadratic Formula Applications
Physics
Calculate projectile motion, free fall, and parabolic trajectories.
Engineering
Solve optimization problems and design parabolic structures.
Finance
Model profit/loss curves and break-even analysis.
Education
Learn algebra concepts with step-by-step solutions.
Frequently Asked Questions
The discriminant (b²-4ac) reveals the nature of roots: when positive, there are two distinct real roots; when zero, there's one repeated real root; when negative, there are two complex conjugate roots. The larger the discriminant, the further apart the roots are.