Quadratic Equation Solver

Solve quadratic equations (ax² + bx + c = 0). Find roots, discriminant, vertex, and axis of symmetry with a visual graph.

a (x² coefficient)

b (x coefficient)

c (constant)

Root 1 (x₁)

Root 2 (x₂)2

Discriminant (b²-4ac)1

Vertex(2.5, -0.25)

Axis of Symmetry2.5

Nature of RootsTwo distinct real roots

Root 1 (x₁)

How to Use This Calculator

Start by filling in the input fields below. Results update instantly as you type, so you can experiment with different values to see how they affect the outcome.
a (x² coefficient) — Coefficient a in the equation. Accepts values from -100 to 100 (default: 1).
b (x coefficient) — Coefficient b in the equation. Accepts values from -100 to 100 (default: -5).
c (constant) — Coefficient c in the equation. Accepts values from -100 to 100 (default: 6).
Once all inputs are set, review your results in the Results panel. Here's what each output means:
Root 1 (x₁) — your calculated result. This is the primary result of this calculator.
Root 2 (x₂) — your calculated result.
Discriminant (b²-4ac) — your calculated result.
Vertex — your calculated result.
Axis of Symmetry — your calculated result.
Nature of Roots — your calculated result.
View the Parabola Graph below for a visual breakdown of how the numbers relate to each other.
Explore the related calculators below if you need deeper analysis or want to approach this topic from a different angle.

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Formula

x = (-b ± √(b² - 4ac)) / 2a

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