What is Quadratic Calculator?
This quadratic calculator runs locally in your browser. Enter the coefficients a, b and c of the standard form ax²+bx+c=0 and it instantly computes: the discriminant Δ=b²−4ac (Δ>0 two real roots, Δ=0 one repeated root, Δ<0 two complex roots), both roots x₁ and x₂ (including complex form), the vertex (−b/2a, (4ac−b²)/4a), and Vieta relations x₁+x₂=−b/a, x₁·x₂=c/a. Negative, decimal and fractional coefficients are supported. Everything runs locally — nothing is uploaded. Built for homework checks, teacher question verification and engineering math.
▶Use Cases5 scenarios
- ◆Checking quadratic homework answers
- ◆Solving quadratics with complex roots
- ◆Finding parabola vertex and axis of symmetry
- ◆Teaching the three discriminant cases
- ◆Parabola math in engineering and physics
▶How to Use5 steps
- 1Enter coefficient a (must not be 0)
- 2Enter coefficients b and c
- 3Read the discriminant Δ to see the root type
- 4Read roots x₁ and x₂ (real or complex)
- 5Check the vertex and Vieta relations, copy results
▶Features8 features
- ✓Free
- ✓No signup
- ✓Real-time solving
- ✓Automatic discriminant check
- ✓Complex root support
- ✓Vertex and Vieta relations
- ✓Fractional coefficients
- ✓100% local
▶FAQ7 questions
What is a quadratic calculator?
An online algebra tool. Input: coefficients a, b, c of ax²+bx+c=0. Output: discriminant, real or complex roots, vertex coordinates and Vieta relations. Used for homework checks, teaching and engineering. Everything runs locally — no uploads.
What is the discriminant and how does it determine roots?
Δ=b²−4ac. If Δ>0 the equation has two distinct real roots; if Δ=0 one repeated root; if Δ<0 two conjugate complex roots.
What if a equals 0?
With a=0 the equation degenerates to the linear form bx+c=0, and the tool prompts you to enter a valid quadratic coefficient a≠0.
Does it support fractions or decimals?
Yes. Decimals (e.g. 1.5) and fractions (e.g. 3/4) are both accepted and parsed automatically.
How is the vertex calculated?
The vertex x-coordinate is −b/(2a); substituting it back gives y=(4ac−b²)/(4a) — the parabola's maximum or minimum point.
What are Vieta relations?
The sum of the roots x₁+x₂=−b/a and the product x₁·x₂=c/a. Both hold even when the roots are complex.
Is my data uploaded?
No. All calculation happens locally in your browser with no network requests.