Quadratic Formula
Solve ax² + bx + c = 0 and see the parabola with roots and vertex labeled
1x² + (−3)x + (2) = 0 | x = (−b ± √(b²−4ac)) / 2a
Discriminant
1
Vertex
(1.5, -0.25)
Roots
Root 1
1
Root 2
2
Parabola opens
upward
About this calculator
The Quadratic Formula Calculator solves any equation of the form ax² + bx + c = 0 and shows the roots, discriminant, and parabola vertex. It handles equations with two real roots, one repeated root, or no real roots. Use it for algebra homework, engineering calculations, or physics problems.
Common examples
- x² − 5x + 6 = 0 (a=1, b=−5, c=6) → roots x = 3 and x = 2
- 2x² + 4x − 6 = 0 (a=2, b=4, c=−6) → roots x = 1 and x = −3
- x² − 2x + 1 = 0 (a=1, b=−2, c=1) → one double root x = 1
- x² + 1 = 0 (a=1, b=0, c=1) → no real roots (complex)
- 3x² − 12x + 9 = 0 (a=3, b=−12, c=9) → roots x = 3 and x = 1