# Algebra II

Your studies in algebra 1 have built a solid foundation from which you can explore linear equations, inequalities, and functions. In algebra 2 we build upon that foundation and not only extend our knowledge of algebra 1, but slowly become capable of tackling the BIG questions of the universe. We'll again touch on systems of equations, inequalities, and functions...but we'll also address exponential and logarithmic functions, logarithms, imaginary and complex numbers, conic sections, and matrices. Don't let these big words intimidate you. We're on this journey with you!

## Manipulating functions

A great cook knows how to take basic ingredients and prepare a delicious meal. In this topic, you will become function-chefs! You will learn how to combine functions with arithmetic operations and how to compose functions. You will also learn how to transform functions in ways that shift, reflect, or stretch their graphs. Finally, you will learn about inverse functions and how to find them!

## Introduction to complex numbers

Learn about complex numbers and how to add, subtract, and multiply them. This will come in useful when working with polynomials.

## Arithmetic with polynomials

Learn how to add, subtract, multiply, and even divide polynomials.

## Polynomial expressions, equations, and functions

Learn how to manipulate polynomials in order to prove identities and find the zeros of those polynomials. Use this knowledge to solve polynomial equations and graph polynomial functions. Learn about symmetry of functions.

## Radical equations and functions

In this topic you will learn how to solve radical equations (which are equations with radical expressions in them) while avoiding extraneous solutions. You will also learn how to graph radical functions.

## Rational expressions, equations, and functions

Rational expressions are like fractions, but instead of integers in the numerator and the denominator, you have variable expressions! Learn how to work with such expressions. Namely, simplify, add, subtract, multiply, and divide them (much like fractions!). Then, solve some equations with rational expressions in them, and analyze the behavior of rational functions.

## Exponential growth and decay

Learn how to analyze and manipulate exponential functions and expressions in order to study their rate of change.

## Exponential and logarithmic functions

Learn about logarithms, which are the inverses of exponents. Use logarithms to solve various equations. Then analyze both logarithmic and exponential functions and their graphs.

## Trigonometric functions

Learn about the definition of the basic trigonometric functions (sin(x), cos(x), and tan(x)), and use advanced trigonometric functions for various purposes.

## Advanced equations and inequalities

Learn how to approximate the solution to any kind of equation by graphing; Learn how to solve non-linear inequalities; Learn how to solve systems with more than two equations.

## Advanced functions

Learn how to determine the domain, the range, and the graph of relatively advanced functions. Learn how to interpret advanced features of functions (like symmetry, end behavior, and periodicity) in terms of their context, and compare features of various types of functions. Learn about two-variable functions.

## Sequences and series

Review sequences and then dive into arithmetic and geometric series.

## Modeling with algebra

Practice modeling problems with a variety of function types.

## Introduction to conic sections

Learn about two basic conic sections and their equations: Circle and Parabola.