Quadratic
Calculator

Solve ax² + bx + c = 0. Get roots, discriminant, vertex, axis of symmetry, and a live parabola graph.

Coefficients

Equation

x² - 2x + 1 = 0

Discriminant (Δ = b² − 4ac)

0Zero

Roots

1 (double root)

Vertex

(1, 0)

Axis of Symmetry

x = 1

Y-Intercept

(0, 1)

Opens

Upward

Increasing

x ≥ 1

Decreasing

x ≤ 1

Positive (f(x) > 0)

x ≠ 1

Negative (f(x) < 0)

None

Parabola Graph

Learn more

The quadratic formula has been known since Babylon — how was it discovered?

Was this useful?

Related Tools

Interest Calculator

Calculate simple and compound interest on savings and investments with yearly breakdown.

Speed Distance Time Calculator

Calculate speed, distance, or time given the other two values with multiple unit conversions.

Base Calculator

Convert between binary, octal, decimal, and hex. Perform arithmetic in any base with 32-bit two's complement support.

Percentage Calculator

Calculate percentages four ways: X% of Y, what percent X is of Y, X is Y% of what, and percentage change.

Random Number Generator

Generate cryptographically random numbers with custom range, count, and duplicate controls.

Sales Tax Calculator

Calculate sales tax, pre-tax price, and total for any tax rate. Add tax to a price or extract tax from a tax-inclusive total.

Frequently Asked Questions

The quadratic formula solves equations of the form ax squared plus bx plus c equals zero. The solution is x equals negative b plus or minus the square root of (b squared minus 4ac), all divided by 2a.

The discriminant is the value b squared minus 4ac inside the square root of the quadratic formula. A positive discriminant means two real roots, zero means one repeated real root, and a negative discriminant means two complex roots.

The x-coordinate of the vertex is found using x equals negative b divided by 2a. Substituting this x value back into the equation gives the y-coordinate of the vertex.

Quadratic Calculator - Solve ax² + bx + c = 0 | ToolsCanvas