Quadratic Formula Calculator
Roots, vertex and discriminant for ax² + bx + c.
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Results
- Roots
- x = 3, x = 2
- Discriminant
- 1 — two real roots
- Vertex
- (2.5, -0.25)
- Axis of symmetry
- x = 2.5
Working
- 1Discriminant = -5² − 4(1)(6) = 1
Quick answer
The quadratic formula gives x = (−b ± √(b² − 4ac)) ÷ 2a; the discriminant b² − 4ac tells you how many real roots exist.
x = (−b ± √(b² − 4ac)) ÷ 2a
How to use the Quadratic Formula Calculator
- 1Enter the coefficients a, b and c.
- 2Read the roots and discriminant.
- 3Use the vertex to sketch the parabola.
Frequently asked questions
What does the discriminant tell me?
Positive means two real roots, zero means one repeated root, negative means the parabola never crosses the x-axis.
Can I always factor instead?
Only when roots are rational. The formula works for every quadratic, factorable or not.