Quadratic Formula Calculator — Step-by-Step Roots & Graph
Free quadratic formula calculator. Solves ax² + bx + c = 0 with real and complex roots, discriminant analysis, vertex coordinates, and interactive parabola plot.
How to use this calculator
👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉
In plain English — what does this do?
🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.
The Quadratic Formula Calculator finds the roots (x-intercepts) of any second-degree polynomial equation ax² + bx + c = 0, calculating both real and imaginary/complex solutions, the discriminant, and the parabola's vertex.
What is Quadratic Formula Calculator — Step-by-Step Roots & Graph?
The Quadratic Formula Calculator finds the roots (x-intercepts) of any second-degree polynomial equation ax² + bx + c = 0, calculating both real and imaginary/complex solutions, the discriminant, and the parabola's vertex.
How to use it
- 1️⃣ Enter the coefficients a, b, and c (where a ≠ 0).
- 2️⃣ Inspect the discriminant Δ = b² - 4ac to determine root nature (two real roots, one repeated root, or two complex conjugate roots).
- 3️⃣ Review the exact roots and step-by-step algebraic substitution.
- 4️⃣ Check the parabola vertex, axis of symmetry, and visual graph plot.
Formula
💡 See it in action — a real example
❓ Common questions
- What does the discriminant tell you?
- If Δ > 0, the equation has two distinct real roots. If Δ = 0, there is exactly one repeated real root. If Δ < 0, there are two complex roots containing the imaginary unit i.
- Why can't coefficient 'a' equal 0?
- If a = 0, the x² term disappears, reducing the polynomial to a linear equation bx + c = 0 rather than a quadratic.
- What is the vertex of a parabola?
- The vertex is the extremum point (absolute minimum if a > 0, absolute maximum if a < 0) located at x = -b / (2a).