Quadratic Formula Calculator

Solve quadratic equations using the quadratic formula.

Enter Coefficients

ax² + bx + c = 0

a (x² coefficient)

b (x coefficient)

c (constant)

Enter your values above and tap Calculate to see the result.

Your Results

Root x₁

Root x₂

Vertex

Axis of Symmetry

Y-intercept

Step-by-step Solution

Parabola: y =

Quadratic Formula

x = (−b ± √(b²−4ac)) / 2a
Δ = b² − 4ac

Δ > 0: 2 distinct real roots
Δ = 0: 1 repeated real root
Δ < 0: 2 complex conjugate roots

Vertex: (−b/2a, f(−b/2a))
Opens up: a > 0 Opens down: a < 0

Quick Examples

Related Calculators

Pro Tips

Results update as you type — change any field to see the effect immediately.

Check that every value uses the same unit before comparing results.

Use the copy button to paste the quadratic formula figures into a note or spreadsheet.

Nothing is sent to a server, so you can use this with private figures.