Algebra 2 | Index

Algebra 2 builds on Algebra 1 with new kinds of functions and equations. It covers transformations and inverses, complex numbers, polynomials, radicals, rational functions, logarithms and series.

It’s for high school Algebra 2 students and anyone preparing for precalculus. Together with Precalculus, it also covers a college algebra course.

What to know first: Algebra 1, especially factoring, quadratic equations and exponent rules. Most students take Geometry before Algebra 2.

Every lesson in this course is live. The list below shows them all in teaching order.

Units in this course

Unit 1: Functions, Transformations and Inverses

  1. Parent Functions — the graphs, domains, ranges and key points of the basic function families
  2. Transformations of Functions — shift, stretch and reflect the graphs of parent functions
  3. Absolute Value Functions — graph absolute value functions and their transformations
  4. Piecewise Functions — evaluate and graph functions defined in pieces
  5. Function Operations — add, subtract, multiply and divide functions
  6. Composition of Functions — put one function inside another and evaluate the result
  7. Inverse Functions — find and graph inverses, and check them with composition

Unit 2: Systems in Three Variables

  1. Systems of Equations in Three Variables — solve three equations with three unknowns by elimination
  2. Linear Programming — find the maximum or minimum of a quantity under several limits

Unit 3: Quadratics and Complex Numbers

  1. Complex Numbers — the imaginary unit i and numbers in a + bi form
  2. Operations with Complex Numbers — add, subtract and multiply complex numbers
  3. Dividing Complex Numbers — use complex conjugates to divide
  4. Complex Solutions of Quadratic Equations — solve quadratics whose solutions are not real
  5. Quadratic Inequalities — solve and graph inequalities with a squared term
  6. Nonlinear Systems of Equations — solve systems that include a parabola, circle or other curve

Also see: factoring, completing the square and the quadratic formula in Algebra 1, Unit 9.

Unit 4: Polynomial Functions

  1. End Behavior of Polynomials — use the degree and leading coefficient to describe a graph’s ends
  2. Polynomial Long Division — divide polynomials the way you divide numbers
  3. Synthetic Division — a shortcut for dividing by a linear factor
  4. Remainder and Factor Theorems — use the remainder to test factors and evaluate polynomials
  5. Sum and Difference of Cubes — factor sums and differences of two cubes
  6. Solving Polynomial Equations — solve higher-degree equations by factoring
  7. Rational Root Theorem — list possible rational zeros and test them
  8. Fundamental Theorem of Algebra — count all zeros of a polynomial, including complex and repeated ones
  9. Graphing Polynomial Functions — sketch a graph from its zeros, multiplicity and end behavior

Unit 5: Radicals and Rational Exponents

  1. nth Roots — evaluate and simplify cube roots, fourth roots and other roots
  2. Rational Exponents — rewrite between radicals and fractional exponents and simplify
  3. Radical Functions — graph square root and cube root functions
  4. Solving Radical Equations — isolate the radical, raise both sides to a power and check for extraneous solutions

Unit 6: Rational Expressions and Functions

  1. Inverse Variation — relationships where the product of two quantities stays the same
  2. Simplifying Rational Expressions — factor and cancel, and note the excluded values
  3. Multiplying and Dividing Rational Expressions — factor first, then multiply or divide and simplify
  4. Adding and Subtracting Rational Expressions — find a common denominator with variables
  5. Complex Rational Expressions — simplify fractions that contain rational expressions
  6. Solving Rational Equations — clear the denominators and check for extraneous solutions
  7. Graphing Rational Functions — find vertical and horizontal asymptotes and holes, then graph

Unit 7: Exponential and Logarithmic Functions

  1. The Number e — the natural base e and continuously compounded interest
  2. Logarithms — what a logarithm is and how to switch between log and exponential form
  3. Graphing Logarithmic Functions — graph log functions as inverses of exponential functions
  4. Properties of Logarithms — the product, quotient and power rules and the change of base formula
  5. Solving Exponential Equations — use logarithms when the bases don’t match
  6. Solving Logarithmic Equations — rewrite in exponential form and check for extraneous solutions

Unit 8: Sequences and Series

  1. Sigma Notation — write and evaluate sums with sigma notation
  2. Arithmetic Series — add up the terms of an arithmetic sequence
  3. Geometric Series — add up the terms of a finite geometric sequence
  4. Infinite Geometric Series — decide whether an infinite series has a sum and find it

Also see: arithmetic and geometric sequences in Algebra 1, Units 4 and 6.

For Teachers: Standards Alignment

Lessons follow the Common Core high school Algebra 2 standards. Trig functions (the unit circle, radians and sine and cosine graphs) are taught in Trigonometry. Statistics topics, such as the normal distribution and margin of error, are taught in Statistics.

Previous course: Geometry Index · Next course: Trigonometry Index