# 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!

- Combining functions
- Composing functions
- Shifting functions
- Stretching functions
- Modeling situations by combining and composing functions
- Introduction to inverses of functions

## Systems of equations and inequalities

What happens when we have many variables but also many constraints.

## Arithmetic with polynomials

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

- Adding and subtracting polynomials
- Multiplying polynomials
- Long division of polynomials
- Synthetic division of polynomials
- Practice dividing polynomials with remainders
- Polynomial Remainder Theorem

## Polynomial functions

Exploring quadratics and higher degree polynomials. Also in-depth look at rational functions.

- Factoring quadratics
- Completing the square and the quadratic formula
- Quadratic inequalities
- Factoring and roots of higher degree polynomials
- Polynomial graphs and end behavior
- Binomial theorem

## 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 and about the inverse relationship between polynomial and 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.

- Simplifying rational expressions
- Multiplying and dividing rational expressions
- Adding and subtracting rational expressions
- Solving rational equations
- Direct and inverse variation
- End behavior of rational functions

## Logarithms

Log-a-what? No, this tutorial is about neither chopped wood nor music (actually logarithms do have applications in music), but it is fascinating nonetheless.
You know how to take an exponent. Now you can think about what exponent you have to raise a number to to get another number. Yes, I agree--unstoppable fun for the whole family. No, seriously, logarithms are used everywhere (including to measure earthquakes and sound).

## Exponential and logarithmic functions

A look at exponential and logarithmic functions including many of their properties and graphs.

- Exponential growth and decay
- Modeling with exponential functions
- Logarithmic functions
- Logarithmic equations
- Continuous compounding and e

## Advanced functions

Revisiting what a function is and how we can define and visualize one.

- Function introduction
- Domain and range
- Recognizing functions
- Piecewise functions
- Properties and features of functions
- Comparing and interpreting functions

## Imaginary and complex numbers

Understanding and solving equations with imaginary numbers.

## Conic sections

A detailed look at shapes that are prevalent in science: conic sections

## Matrices

## Miscellaneous

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