Algebra Calculators
30 free algebra calculators in Math.
- Completing the SquareRewrite ax²+bx+c into vertex form a(x−h)²+k and identify the vertex coordinates.
- Composite Function CalculatorCompute (f∘g)(x) = f(g(x)) by evaluating two functions in sequence at a given x value.
- Cubic Equation SolverFind all three roots of ax³+bx²+cx+d=0 using the depressed-cubic method, including complex roots.
- Domain CalculatorEstimate the domain of f(x) by sampling the expression parser across a wide range of x values.
- Exponent CalculatorRaise any base to any power, including negative and fractional exponents.
- FOIL CalculatorMultiply two binomials (ax+b)(cx+d) using the FOIL method with step-by-step breakdown.
- Function CalculatorEvaluate a mathematical function f(x) at a given value using the built-in expression parser.
- Function OperationsCompute (f+g)(x), (f−g)(x), (f·g)(x) and (f/g)(x) for two expressions at a given x.
- Half-Life CalculatorSolve exponential decay for half-life, mean lifetime, decay constant or remaining quantity.
- Inverse Function CalculatorNumerically approximate f⁻¹(y) by finding x where f(x)=y using bisection search.
- Linear Equation SolverSolve ax + b = 0 for x, showing the solution and verification step.
- Logarithm CalculatorCompute logarithms in any base, plus natural log and antilog.
- Matrix CalculatorAdd, multiply, transpose and invert matrices, and find determinants.
- Number Sequence CalculatorFind terms and sums of arithmetic, geometric and Fibonacci sequences.
- Piecewise Function CalculatorEvaluate a piecewise-defined function at x by selecting the matching interval branch.
- Polynomial DivisionDivide one polynomial by another using synthetic or long division, showing quotient and remainder.
- Polynomial ExpansionExpand (ax+b)^n using the binomial theorem, showing each term and coefficient.
- Polynomial FactorizationFactor a polynomial into linear factors over the rationals using the rational root theorem.
- Polynomial RootsFind all real and complex roots of a polynomial up to degree 4 using exact algebraic methods.
- Polynomial SolverFind rational roots of a polynomial up to degree 6 using the rational root theorem.
- Quadratic Formula CalculatorSolve any quadratic equation with real or complex roots, vertex and discriminant.
- Quartic Equation SolverSolve ax⁴+bx³+cx²+dx+e=0 for all four roots via Ferrari's resolvent-cubic method.
- Radical SimplifierSimplify √n by extracting the largest perfect-square factor: √n = a√b.
- Range CalculatorEstimate the range of f(x) by evaluating it across its domain and reporting observed min/max.
- Ratio CalculatorSimplify ratios, solve proportions and scale ratios up or down.
- Rational Expression SimplifierAdd, subtract, multiply or divide two rational expressions (fractions of polynomials).
- Root CalculatorFind square roots, cube roots and any nth root of a number.
- Simultaneous Equation SolverSolve a system of two linear equations in two unknowns using Cramer's rule.
- Slope CalculatorFind the slope, angle and line equation through two points.
- Trigonometry CalculatorEvaluate all six trig functions and their inverses in degrees or radians.