SWETAxAI MATHEMATICS LABS
Interactive mathematics tools built to help students explore, visualise, calculate, and understand.
SWETAxAI Mathematics Labs bring together interactive calculators, visualisers, graphing tools, geometry explorers, formula tools, and exam-focused practice in one focused learning environment.
Designed across school mathematics, IGCSE, AS/A Level, Additional Mathematics, and IIT-JEE, the Labs turn abstract mathematical ideas into something students can see, manipulate, test, and apply.
Explore Mathematics. Build Understanding. Solve with Confidence.
SWETAxAI — Smart Tools. Stronger Concepts. Better Results.
SWETAXAI — QUADRATICS & EQUATIONS LAB
Explore quadratics. Analyse equations. Understand roots.
SWETAxAI — Quadratics & Equations Lab is an interactive mathematics environment designed to help students explore quadratic equations and functions through graphs, roots, discriminants, inequalities, parameters, and algebraic relationships.
Move beyond simply applying formulas. Visualise how equations behave, investigate how coefficients affect graphs, and connect algebraic solutions with graphical representations.
Explore & Analyse
- Quadratic Graph Explorer — Visualise quadratic functions and investigate their key features.
- Equation Solver — Solve quadratic equations and explore their solutions.
- Discriminant Explorer — Understand how the discriminant determines the nature of roots.
- Nature of Roots — Explore real, repeated, and complex-root cases.
- Quadratic Inequality Solver — Investigate solution regions for quadratic inequalities.
- Parameterised Quadratic Explorer — Change coefficients and observe how the graph and roots respond.
- Completing the Square — Explore the connection between standard and vertex forms.
- Roots–Coefficients Relationships — Connect roots with the coefficients of a quadratic equation.
- Factor & Remainder Theorem — Explore polynomial factors and remainders interactively.
- Equation Transformation Lab — Investigate how algebraic transformations affect equations and their solutions.
Learn Through Interaction
The Lab connects equations, graphs, roots, and algebraic structure so students can see why mathematical results occur—not simply memorise procedures.
Ideal for school mathematics, IGCSE, Additional Mathematics, AS/A Level, and IIT-JEE preparation.
Fully standalone HTML — no external libraries required.
No sign-up. No installation. No time limit.
Open the Lab and start exploring immediately.
Explore. Analyse. Solve. Understand.
SWETAxAI — Smart Tools. Stronger Concepts. Better Results.
SWETAxAI Quadratic Equation Solver & Visualiser
Explore premium standalone SWETAxAI Quadratic Equation Solver & Visualiser.
It includes:
- Quadratic equation solver
- Discriminant analysis
- Real & complex roots
- Axis of symmetry
- Vertex
- Interactive parabola visualisation
- x-intercepts
- Worked solution steps
- Preset examples
- Responsive mobile-friendly design
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Quadratic Graph Explorer
Explore premium standalone SWETAxAI Quadratic Graph Explorer.
It includes:
- Interactive a, b, c controls
- Live parabola visualisation
- Vertex and axis of symmetry
- Real-root detection
- Opening direction
- y-intercept
- Discriminant interpretation
- Show/hide grid, axis, roots and vertex
- Preset quadratic examples
- Responsive premium interface
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Nature of Roots Explorer
Explore premium standalone SWETAxAI Nature of Roots Explorer.
It includes:
- Discriminant calculator
- Δ > 0: two distinct real roots
- Δ = 0: repeated real root
- Δ < 0: complex conjugate roots
- Visual parabola showing the relationship with the x-axis
- Vertex and discriminant
- Root values
- Factor form where applicable
- Step-by-step reasoning
- Preset examples
- Live updating
- Responsive design
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Discriminant Visualiser
Explore premium standalone SWETAxAI Discriminant Visualiser.
It includes:
- Interactive a, b, c coefficients
- Live discriminant calculation
- Visual Δ < 0 / Δ = 0 / Δ > 0 indicator
- Root classification
- Real and complex roots
- Parabola visualisation
- Vertex and axis of symmetry
- Interactive c-sweep slider
- Step-by-step discriminant calculation
- Preset examples for all three discriminant cases
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Quadratic Inequality Solver
Explore premium standalone SWETAxAI Quadratic Inequality Solver.
It includes:
- Solve ax² + bx + c > 0
- ≥ 0, < 0, ≤ 0
- Discriminant & critical-point analysis
- Interval notation / inequality answer
- Sign-chart reasoning
- Real-root and repeated-root handling
- No-real-root cases
- Visual parabola
- Number-line style solution region
- Open/closed endpoint logic
- Preset examples
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Parameterised Quadratic Explorer
Explore premium standalone SWETAxAI Parameterised Quadratic Explorer.
It includes:
- Multiple parameterised quadratic families
- Interactive parameter k slider
- Exact k input
- Live graph transformation
- Vertex and axis of symmetry
- Discriminant
- Root behaviour
- Automatic identification of complex/no-real-root cases
- Preset parameter values
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Completing the Square Visualiser
Explore premium standalone SWETAxAI Completing the Square Visualiser.
It includes:
- Enter any quadratic ax² + bx + c
- Step-by-step completing-the-square process
- Factor out a automatically
- Calculate the required square term
- Add and subtract the same quantity
- Convert to vertex form
- Vertex and axis of symmetry
- Minimum / maximum identification
- Interactive parabola visualisation
- Preset examples
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Simultaneous Equations Solver
Explore premium standalone SWETAxAI Simultaneous Equations Solver.
It includes:
- Two linear equations in two variables
- Automatic solving for x and y
- Determinant method
- Cramer’s Rule calculations
- Unique solution
- No solution — parallel lines
- Infinitely many solutions — coincident lines
- Interactive graphical intersection
- Line slopes
- Step-by-step reasoning
- Preset examples
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Polynomial Equation Solver
Explore premium standalone SWETAxAI Polynomial Equation Solver.
It includes:
- Polynomial equations up to degree 4
- Quadratic, cubic and quartic modes
- Real and complex roots
- Repeated-root detection and multiplicity
- Complete root set
- Polynomial graph with real x-intercepts
- Automatic degree detection
- Preset examples
- Step-by-step solution structure
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Factor & Remainder Theorem Explorer
Explore premium standalone SWETAxAI Factor & Remainder Theorem Explorer.
It includes:
- Remainder Theorem: P(r)
- Factor Theorem
- Polynomial degree 2–4
- Interactive divisor (x − r)
- Synthetic division / Horner structure
- Quotient and remainder
- Automatic factor / non-factor classification
- Graphical verification at x = r
- Step-by-step reasoning
- Preset examples
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Equation Transformation Lab
Explore premium standalone SWETAxAI Equation Transformation Lab.
It includes:
- Add/subtract transformations
- Multiply/divide transformations
- Expanding brackets
- Quadratic factorisation
- Completing the square
- Linear equation rearrangement
- Step-by-step transformation display
- Equivalent-equation verification
- Solution comparison
- Graphical verification
- Preset examples
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAXAI — FUNCTIONS LAB
Explore functions. Visualise graphs. Understand concepts.
SWETAxAI — Functions Lab is an interactive mathematics environment designed to help students explore functions through graphs, parameters, tables, transformations, and key mathematical properties.
Move beyond static examples and see how functions behave. Change parameters, compare graphs, investigate patterns, and build a deeper understanding of function relationships.
Explore & Analyse
- Plot Functions — Visualise functions directly on interactive coordinate graphs.
- Adjust Parameters — See how changing coefficients and constants transforms a function.
- Compare Functions — Explore similarities and differences between functions.
- Tables of Values — Connect algebraic expressions with numerical and graphical representations.
- Function Properties — Investigate domain, range, intercepts, turning points, symmetry, and intervals.
- Transformations — Explore translations, reflections, stretches, and compressions.
- Practice & Apply — Strengthen understanding through focused mathematical exploration.
Built for Independent Learning
Functions Lab is designed to make abstract function concepts visual, interactive, and intuitive, supporting students from concept discovery through problem solving.
Fully standalone HTML
No external libraries required.
No sign-up. No installation. No time limit.
Just open the tool and start exploring.
Explore Functions. Build Understanding. Solve with Confidence.
SWETAxAI — Smart Tools. Stronger Concepts. Better Results.
SWETAxAI Function Transformation Explorer
Explore premium SWETAxAI Function Transformation Explorer.
It includes:
- Live original vs transformed graphs
- g(x)=af(b(x−h))+k
- 8 function families
- Horizontal/vertical scaling
- Reflections
- Horizontal/vertical translations
- Quick transformation presets
- Automatic transformation interpretation
- Responsive premium interface
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Composite Functions Calculator
Explore premium SWETAxAI Composite Functions Calculator.
It includes:
- f(g(x)), g(f(x)), f(f(x)), g(g(x))
- Symbolic composition workflow
- Step-by-step substitution
- Numerical evaluation
- Composition-order comparison
- Domain-aware error handling
- Responsive premium UI
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Inverse Function Explorer
Explore premium SWETAxAI Inverse Function Explorer.
It includes:
- Linear, quadratic, cubic, square-root and reciprocal functions
- Automatic inverse construction
- One-to-one / invertibility checks
- Quadratic domain restriction handling
- Step-by-step inverse derivation
- Numerical verification of inverse compositions
- Interactive f(x), f−1(x), and y=x graph
- Domain and range interpretation
- Responsive premium UI
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Domain & Range Finder
Explore premium SWETAxAI Domain & Range Finder.
It includes:
- Linear, quadratic, square-root, reciprocal, rational, logarithmic, exponential and absolute-value functions
- Automatic domain restrictions
- Automatic range determination
- Interval notation
- Algebraic reasoning for each restriction
- Interactive graph
- Adjustable graph window
- Responsive premium interface
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Function Graphing Lab
Explore premium SWETAxAI Function Graphing Lab.
It includes:
- Quadratic, linear, cubic
- Absolute value
- Square root
- Reciprocal
- Exponential
- Logarithmic
- Sine & cosine
- Adjustable x/y viewing windows
- Automatic undefined-point breaks
- Coordinate grid and axes
- Function value readout
- Mathematical interpretation panel
- Responsive premium design
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Modulus Function Graph Explorer
Explore premium SWETAxAI Modulus Function Graph Explorer.
It includes:
- y=a∣x−h∣+k
- y=∣ax+b∣+k
- y=∣ax2+bx+c∣
- Interactive coefficient controls
- Automatic vertex detection
- Opening direction
- x-intercept detection
- Piecewise interpretation
- Adjustable coordinate-plane window
- Live graphing
- Transformation insights
- Responsive premium UI
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Piecewise Function Explorer
Explore premium SWETAxAI Piecewise Function Explorer.
It includes:
- 3 configurable function pieces
- Adjustable boundary points a and b
- Linear expressions for each interval
- Automatic piece selection for any input x
- Piecewise notation display
- Interactive graph
- Open/closed boundary points
- Continuity checks at both boundaries
- Left-hand, right-hand and actual function values
- Domain interpretation
- Mathematical insight panel
- Responsive premium interface
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Function Composition Visualiser
Explore premium SWETAxAI Function Composition Visualiser.
It includes:
- f(x)=ax+b and g(x)=cx+d
- Interactive f(g(x)) and g(f(x))
- Visual input → function → intermediate value → output flow
- Step-by-step composition mapping
- Symbolic composition results
- Numerical evaluation
- Side-by-side comparison of both composition orders
- Demonstration that composition is generally not commutative
- Responsive premium interface
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Parameterised Function Explorer
Explore premium SWETAxAI Parameterised Function Explorer.
It includes:
- Quadratic family y=a(x−h)2+k
- Linear family y=ax+b
- Modulus family y=a∣x−h∣+k
- Exponential family
- Reciprocal family
- Live parameter sliders
- Real-time graph transformation
- Function evaluation at any x
- Automatic key-point / asymptote identification
- Behaviour classification
- Parameter-by-parameter mathematical interpretation
- Adjustable graph scale
- Responsive premium interface
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Function Iteration Explorer
Explore premium SWETAxAI Function Iteration Explorer.
It includes:
- Linear iteration xn+1=axn+b
- Quadratic iteration xn+1=(xn)^2+c
- Modulus iteration
- Logistic iteration
- Adjustable initial value x0
- Adjustable number of iterations
- Full iteration table
- Final value and change per iteration
- Convergence / divergence / possible-cycle detection
- Fixed-point explanation
- f(x) vs. y=x visualisation
- Cobweb-style iteration path
- Mathematical interpretation
- Responsive premium interface
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.
SWETAxAI Function Equation Solver
Explore premium SWETAxAI Function Equation Solver.
It includes:
- Linear equations
- Quadratic equations + discriminant
- Modulus equations
- Square-root equations
- Exponential equations
- Logarithmic equations
- Reciprocal equations
- Analytical solution methods
- Domain checks
- Automatic solution verification
- Graphical solution visualization
- Multiple-solution handling
- Responsive premium interface
- Fully standalone HTML — no external libraries required
- No sign-up, no installation, and no time limit.