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Algebra 2

x²

Algebra 2

Quadratics, polynomials, exponentials, and logarithms

269Modules

11Units

Recommended preparation

We recommend a solid grasp of Algebra 1 — solving equations, graphing lines, and working with exponents.

The Undo ButtonINTRO

Function ZooINTRO

Parent Functions CatalogLESSON

Analyzing f(x) = 2√(x - 3) + 1EXAMPLE

Function Transformer LabACTIVITY

Piecewise Function GrapherLESSON

Graphing f = {x² if x < 2; 3x - 2 if x ≥ 2}EXAMPLE

Absolute Value as PiecewiseLESSON

Piecewise and Absolute ValuePRACTICE

Piecewise BuilderACTIVITY

Traffic Light FunctionsREAL-WORLD

Combining FunctionsLESSON

Function Arithmetic VisualizedREAL-WORLD

Function CompositionLESSON

Finding (f ∘ g)(x) where f(x) = x² + 1 and g(x) = 2x - 3EXAMPLE

Operations Practice ArenaPRACTICE

Composition MachineACTIVITY

Finding Inverse FunctionsLESSON

Finding the Inverse of f(x) = (2x + 3)/(x - 1)EXAMPLE

One-to-One and InversesPRACTICE

Inverse Function DetectiveACTIVITY

Transformation RecognitionPRACTICE

Functions SummarySUMMARY

Functions ReferenceFORMULA SHEET

Section 1 AssessmentASSESSMENT

Beyond the Real Number LineINTRO

Parabola ArchitectureINTRO

When Parabolas Don't TouchINTRO

The Imaginary Unit iLESSON

Complex Number CalculatorACTIVITY

Complex Operations LabPRACTICE

Complex Solutions PracticePRACTICE

Complex Conjugates and DivisionLESSON

Simplifying (3 + 2i)(4 - 5i)EXAMPLE

Three Forms of QuadraticsLESSON

Advanced QuadraticsPRACTICE

Quadratic Forms ConverterACTIVITY

Converting to Vertex Form by Completing the SquareEXAMPLE

The Discriminant RevealedLESSON

Quadratic Solution AnalyzerACTIVITY

Solving x² - 4x + 13 = 0EXAMPLE

Focus and DirectrixLESSON

Parabola Properties ExplorerACTIVITY

Fundamental Theorem PreviewLESSON

Quadratics and Complex SummarySUMMARY

Quadratics and Complex Numbers ReferenceFORMULA SHEET

Section 2 AssessmentASSESSMENT

Every Polynomial Has RootsINTRO

Roller Coaster PolynomialsINTRO

End Behavior PatternsLESSON

Multiplicity EffectsLESSON

Polynomial Graph SketcherACTIVITY

Polynomial Long DivisionLESSON

Dividing x³ - 2x² - 5x + 6 by (x - 3)EXAMPLE

Synthetic Division ShortcutLESSON

Division Practice LabPRACTICE

Remainder and Factor TheoremsLESSON

Division and TheoremsPRACTICE

Rational Root TheoremLESSON

Fundamental Theorem ApplicationsPRACTICE

Descartes' Rule of SignsLESSON

Zero Finding StrategyLESSON

Finding Zeros of x³ - 2x² - 11x + 12EXAMPLE

Finding Zeros PracticePRACTICE

Polynomial Zero HunterACTIVITY

Statement and ImplicationsLESSON

Graphing y = x³ - 4x² - 7x + 10EXAMPLE

Complex Conjugate TheoremLESSON

Writing Polynomials from RootsEXAMPLE

Polynomial ConstructorACTIVITY

Polynomial Behavior AnalysisPRACTICE

Polynomials SummarySUMMARY

Polynomials ReferenceFORMULA SHEET

Section 3 AssessmentASSESSMENT

Speed vs Time RelationshipsINTRO

Rational Function BasicsLESSON

Rational Function RecognitionPRACTICE

Simple Rational GrapherACTIVITY

Horizontal Asymptote RulesLESSON

Three Types of AsymptotesLESSON

Asymptote ExplorerACTIVITY

Finding All Asymptotes of f(x) = (2x² + 3x - 1)/(x² - 4)EXAMPLE

Holes vs AsymptotesLESSON

Advanced GraphingPRACTICE

Cross-Multiplication and LCDLESSON

Solving 2/(x + 1) + 3/(x - 2) = 1EXAMPLE

Rational InequalitiesLESSON

Analyzing f(x) = (2x + 3)/(x - 1)EXAMPLE

Rational Equations and InequalitiesPRACTICE

Inequality Solution VisualizerACTIVITY

Work Rate ProblemsREAL-WORLD

Rational Functions SummarySUMMARY

Rational Functions ReferenceFORMULA SHEET

Section 4 AssessmentASSESSMENT

Logarithm Rules DiscoveryINTRO

The Number eLESSON

Exponential Model FitterACTIVITY

Natural Exponential FunctionsPRACTICE

Compound Interest Deep DiveREAL-WORLD

The Inverse of ExponentialINTRO

Logarithm DefinitionLESSON

Logarithm EvaluatorACTIVITY

Basic LogarithmsPRACTICE

Common and Natural LogsLESSON

Three Key PropertiesLESSON

Solving log₂(x) + log₂(x - 3) = 2EXAMPLE

Condensing log(x) + 2log(y) - 3log(z)EXAMPLE

Expanding log₃(x²y/z³)EXAMPLE

Properties Practice LabPRACTICE

Logarithm PropertiesPRACTICE

Change of Base FormulaLESSON

Converting Between FormsEXAMPLE

Graphing y = 2e⁻⁰·⁵ˣ + 3EXAMPLE

Solving Exponential EquationsLESSON

Exponential and Log EquationsPRACTICE

Solving Logarithmic EquationsLESSON

Equation Solving StrategistACTIVITY

Solving 3²ˣ⁻¹ = 7ˣ⁺²EXAMPLE

Population PredictionREAL-WORLD

Exponential and Logarithmic SummarySUMMARY

Exponential and Logarithmic ReferenceFORMULA SHEET

Section 5 AssessmentASSESSMENT

Area and Volume ConnectionsINTRO

3D Intersection VisualizerINTRO

Matrix OperationsLESSON

Matrix Operations PracticePRACTICE

Matrix Multiplication MechanicsLESSON

Multiplying [2 3; -1 4] × [1 -2; 3 1]EXAMPLE

Matrix CalculatorACTIVITY

From System to MatrixLESSON

Gaussian EliminationLESSON

Solving Using Row ReductionEXAMPLE

System Solution TypesLESSON

Calculating DeterminantsLESSON

Determinant ExplorerACTIVITY

Cramer's RuleLESSON

Solving a 2×2 System with Cramer's RuleEXAMPLE

Determinants and ApplicationsPRACTICE

Matrix InversesLESSON

Finding the Inverse of [3 2; 5 4]EXAMPLE

Matrix System SolverACTIVITY

Matrix MethodsPRACTICE

Data in Rectangular ArraysREAL-WORLD

Elimination with Three VariablesLESSON

3-Variable System SolverACTIVITY

Solving the System x + y + z = 6, 2x - y + z = ...EXAMPLE

3-Variable SystemsPRACTICE

Systems and Matrices SummarySUMMARY

Systems and Matrices ReferenceFORMULA SHEET

Section 6 AssessmentASSESSMENT

Perfect Round ShapesINTRO

Standard Form of CirclesLESSON

Graphing (x - 3)² + (y + 2)² = 25EXAMPLE

Completing the Square for CirclesLESSON

Converting x² + y² - 6x + 4y - 12 = 0EXAMPLE

Circles PracticePRACTICE

Circle DesignerACTIVITY

Finding Intersections of Circle and LineEXAMPLE

Two Foci DefinitionLESSON

Standard Form of EllipsesLESSON

Graphing x²/25 + y²/9 = 1EXAMPLE

Ellipses PracticePRACTICE

Finding FociLESSON

Ellipse Properties ExplorerACTIVITY

Planetary OrbitsREAL-WORLD

Difference of DistancesLESSON

Standard FormsLESSON

Asymptotes of HyperbolasLESSON

Graphing x²/16 - y²/9 = 1EXAMPLE

Hyperbolas PracticePRACTICE

Hyperbola AnalyzerACTIVITY

Navigation and GPSREAL-WORLD

Standard Form of ParabolasLESSON

Identifying ConicsLESSON

Conic Sections SorterACTIVITY

General ConicsPRACTICE

Rotation of AxesLESSON

Systems of ConicsLESSON

Conic Systems SolverACTIVITY

Conic Sections SummarySUMMARY

Conic Sections ReferenceFORMULA SHEET

Section 7 AssessmentASSESSMENT

Pattern DetectiveINTRO

Sequence NotationLESSON

Recursive FormulasLESSON

Sequence GeneratorACTIVITY

Finding the nth TermEXAMPLE

Sequence BasicsPRACTICE

Sigma NotationLESSON

Special Sum FormulasLESSON

Properties of SummationLESSON

Evaluating Σ(2i² - 3i) from i=1 to 10EXAMPLE

Summation Practice ToolACTIVITY

Summation NotationPRACTICE

Common RatioLESSON

Geometric Series ExplorerACTIVITY

Geometric Sequences and SeriesPRACTICE

Finding Sum of Geometric SeriesLESSON

Infinite Geometric SeriesLESSON

Summing 1 + 1/2 + 1/4 + 1/8 + ...EXAMPLE

Finding Sum of First 20 TermsEXAMPLE

Compound GrowthREAL-WORLD

Common DifferenceLESSON

Gauss's MethodLESSON

Arithmetic Series CalculatorACTIVITY

Arithmetic Sequences and SeriesPRACTICE

Stadium SeatingREAL-WORLD

Sequences and Series SummarySUMMARY

Sequences and Series ReferenceFORMULA SHEET

Section 8 AssessmentASSESSMENT

Ferris Wheel FunctionsINTRO

Radian MeasureLESSON

Unit Circle DefinitionLESSON

Special AnglesLESSON

Unit Circle MasteryPRACTICE

Unit Circle TrainerACTIVITY

Sine and Cosine WavesLESSON

Tangent and Its AsymptotesLESSON

Graphing y = 2sin(3x - π/2) + 1EXAMPLE

Trig Function GrapherACTIVITY

Graphing PracticePRACTICE

When Does Height Equal Zero?REAL-WORLD

Pythagorean IdentityLESSON

Angle Sum FormulasLESSON

Verifying cos(2θ) = 2cos²θ - 1EXAMPLE

Identity VerifierACTIVITY

Basic Trigonometric EquationsLESSON

Solving 2sin²θ - sinθ - 1 = 0EXAMPLE

Trigonometric IdentitiesPRACTICE

Using Identities to SolveLESSON

Solving Trig EquationsPRACTICE

Equation Solver LabACTIVITY

Trigonometry SummarySUMMARY

Trigonometry ReferenceFORMULA SHEET

Section 9 AssessmentASSESSMENT

Menu CombinationsINTRO

Box Plots and HistogramsLESSON

Statistics CalculatorACTIVITY

Measures of CenterLESSON

Measures of SpreadLESSON

Calculating Standard DeviationEXAMPLE

Class Score AnalysisREAL-WORLD

Statistical AnalysisPRACTICE

Distribution ExplorerACTIVITY

Discrete DistributionsLESSON

Distributions PracticePRACTICE

Binomial DistributionLESSON

Finding P(X = 3) for 5 Coin FlipsEXAMPLE

Normal Distribution PreviewLESSON

Expected WinningsREAL-WORLD

Probability RulesLESSON

Solving P(A or B) when Events OverlapEXAMPLE

Conditional ProbabilityLESSON

Probability SimulatorACTIVITY

Probability CalculationsPRACTICE

Dice and CardsREAL-WORLD

Fundamental Counting PrincipleLESSON

Permutations FormulaLESSON

Combinations FormulaLESSON

Finding Number of 3-Letter CodesEXAMPLE

Counting CalculatorACTIVITY

Counting MethodsPRACTICE

Probability and Statistics SummarySUMMARY

Probability and Statistics ReferenceFORMULA SHEET

Section 10 AssessmentASSESSMENT

Mathematical Modeling ShowcasePRACTICE

Start Your BusinessACTIVITY

Course Connections WebSUMMARY

Your Mathematical ToolkitFORMULA SHEET