Quadratic Formula Calculator
Roots, vertex and discriminant for ax² + bx + c.
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ⓘ Live results
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.
Worked example
Using the values the calculator loads with:
Inputs
- a1
- b-5
- c6
Results
- Rootsx = 3, x = 2
- Discriminant1 — two real roots
- Vertex(2.5, -0.25)
- Axis of symmetryx = 2.5
- Discriminant = -5² − 4(1)(6) = 1
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.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.