# Algebra 2 Tutorials

Algebra 2 builds upon previous algebraic concepts such as Powers, Roots, and Radicals and expand to more advanced levels such as Polynomials and Factoring and Conic Sections – Hyperbolas. Sophisticated applications are found in Exponents and Logs where you will develop special scales for measurement, used for the Richter scale for earthquake magnitude, and the pH scale for acidity. Methods for solving Systems of Linear Equations and Inequalities and Rational Functions are covered in our more basic topics which provide strong proficiency to master Matrices and Determinants. Algebra 2 is a highly integrated subject that establishes strong foundational skills and supports mastery at more advanced levels that are sure to challenge you.

## Linear Equations and Functions

Everyone knows that you have to walk before you can run; therefore, we'll be tackling linear equations before moving onto direct variation equations. In Linear Equations and Functions we'll begin by explaining exactly what a function is by going over Functions vs. Relations. Once you have an understanding of what a function is, we'll review the most basic type of function in the form of linear equations. After reviewing linear equations, we'll go over Direct Variation Equations so that you will have a better understanding of slope, which is a concept that will stay with you until Calculus and beyond.

## Equations and Inequalities

In Equations and Inequalities we begin by reviewing how to solve and graph equations and inequalities. After reviewing, we'll focus on working with special types of equations and inequalities involving absolute values. The goal is to help you understand how equations and inequalities can be applied to our everyday lives.

## Systems of Linear Equations and Inequalities

In Systems of Linear Equations and Inequalities we will discuss how to solve a system of equations containing two or more equations through the methods known as Substitution in Linear Equations and Simultaneous Linear Equations. Once you have solving multiple equations under your belt, you will begin working with systems of inequalities. The goal is that you will understand how equations and inequalities can be used to model real world problems.

## Quadratic Equations and Functions

In Quadratic Equations and Functions we will go over different methods for working with quadratic equations. We will demonstrate how to use The Quadratic Formula and Completing the Square to solve a function that might not be recognized as a quadratic equation such as Quadratics with no Bx Term. We will also explain how to use quadratic functions to represent data.

## Conic Sections - Parabolas

By this point in your math career you may be quite familiar with parabolas, but even though they seem simple, some interesting things go on behind the scenes in order for a graph to be considered a parabola. In Conic Sections – Parabolas we will explore the different aspects of The Parabola  to gain a better understanding of the underlying principles governing them. One major aspect of the parabola that we will review is the meaning of The Standard Form Equation For A Parabola and how it is related to the Focus and Directrix of a Parabola.

Concepts: 11
Quiz Points: 165

## Conic Sections - Circles and Ellipses

Which shape is more general, the circle or the ellipse? You may be inclined to say that it is the circle since you have been working with it since kindergarten, but not so fast! In Conic Sections – Circles and Ellipses we will take an in-depth look at The Ellipse and discover why The Graph of a Circle is considered a special case of an ellipse. We will also look at The Standard Equation For An Ellipse which will help graph any circle or ellipse.

## Conic Sections - Hyperbolas

If you’ve ever come across two identical twins you might have a hard time telling them apart. Likewise, before Conic Sections – Hyperbolas you might have had a hard time differentiating between a parabola and a hyperbola. Here our aim is to study The Hyperbola very closely. We will study such things as The Eccentricity of a Hyperbola and learn how to recognize The Graph of a Hyperbola. In the same way you can differentiate between twins by getting to know their personalities, we will differentiate between a parabola and hyperbola by understanding the differences in their behavior.

## Polynomials and Factoring

Ready to earn your higher degree?  In Polynomials and Factoring we will review how to recognize what a polynomial function is and how to work with Higher Degree Polynomials. This lesson teaches you how to recognize a polynomial function when you see one. In addition, we will go over how to determine the behavior of any polynomial and graph that behavior. With this knowledge you will learn how to convey a great deal of information in many different fields such as medicine, aeronautics, and even car racing.

## Powers, Roots, and Radicals

Are your surgical tools ready?  If not, find them quick, because we'll be operating on functions in no time!  In Powers, Roots, and Radicals we will go over polynomial, root, and exponential functions. We will demonstrate how to perform several different operations on these functions including: addition, subtraction, multiplication, and division. We will also go over what it means to take The Function of a Function and what Inverse Functions are. The goal is to help you not only recognize these functions, but be able to perform different types of transformations on them as well.

## Rational Expressions

Have you ever wondered what the difference is between simple algebraic expressions and rational expressions? Or maybe you have wondered what Algebraic Fraction Equations are. No?! Well...you are now! In Rational Expressions we will not only go over what rational expressions are, but how to manipulate and solve them using familiar methods such as multiplication and division and new methods such as Reducing through Basic Factoring.

## Rational Functions

In Rational Expressions you learned what a rational expression is, but you might be asking yourself, “Other than my undying love for all things math, is there another reason to study this subject?” In Rational Functions our aim is to answer this question by observing Rational Functions in the Real World. In addition, we will go over the behavior of rational functions and discuss the relationship between Asymptotes and Rational Functions.

## Exponents and Logs

In Exponents and Logs we will go over how to calculate exponential and logarithmic functions and explain how they are related. To begin with we will go over an Introduction to Logarithms and discuss the many different rules related to logarithms such as The Product Rule for Logarithms. Next we will introduce Exponential Equationsand explain why they are useful. Finally we will explain how to solve exponential functions using logarithms and vise versa.

## Sequences and Series

It is human nature to look for patterns in the world around us. Since the purpose of mathematics is to relate to the world through numbers, it is logical that we try to find patterns in numbers. In Sequences and Series we go over what the Terms in Sequences represent and how to recognize patterns in a sequence or series. Because some patterns are quite complex, we will go over different types of patterns such as Geometric Series and Sequences. This all culminates with us trying to predict future events through the use of mathematical induction.

## Trigonometric Identities

In Trigonometric Identities we will introduce the tools available to you when working with problems involving trigonometric functions. The goal is to not only help you understand how to prove that two sides of an equation are equal, but to make you comfortable with the different Trigonometric Techniques used to relate one trigonometric function to another.

## The Unit Circle

There are six different trigonometric functions that you have been dealing with and each has their own behavior. Often times it can be difficult to remember how a particular function behaves but have no fear, The Unit Circle is here. We will go over what The Unit Circle is and how it can be used to represent trigonometric functions. You may even be moved to tears after understanding the beauty behind the Coordinates on the Unit Circle and how the different trigonometric functions are related to one another.

## Graphing Trigonometric Functions

You have probably observed that if you throwing a rock in water causes ripples. What if you could model these waves by using a Sine Wave or a Cosine Wave?  Remember that mathematics is just a means by which we try to model the world around us in terms of numbers. In Graphing Trigonometric Functions we will explore the different parts of a trigonometric function and show how you can manipulate them to even model ripples of water.

## Trigonometric Equations

Have you ever wondered why a ladder placed against a wall might sometimes slide and at other times stay still? Although this is a physics problem, the physicists turn to mathematicians for a bit of help.  Before you can solve this problem you will need to understand the mathematics behind the equations governing this problem. In Trigonometric Equations we will go over how to do just that by exploring concepts such as Inverse Sine.

## Statistics and Probability

Have you ever wondered how a meteorologist can predict rain fall amounts or the liklihood of a sunny day? A lot of it has to do with Statistics and Probability, where we will be laying the foundation you will need in order to analyze data and make predictions from a set of data. For example, we will go over what the different Measures of Variation are and how finding the mean, median, and mode of a given set of data can help you determine the chances of an event, such as rain, occurring.

## Introduction to Matrices

Neo, Neo, are you there? Could you find your way out of and into the Matrix like Neo did? In Introduction to Matrices we introduce Matrices and demonstrate how they are used to organize data. Once you understand a matrix's different elements we will go over how to perform different types of operations concerning matrices such as Adding and Subtracting Matrices and Matrix Multiplication. This knowledge will serve as your foundation when working with more advanced matrix concepts.

## Matrices

In The Matrix, Neo asks Trinity, "What is the Matrix?" She replies, "The answer is out there, Neo, and it's looking for you, and it will find you if you want it to." In Matrices we will build upon the foundation set in Introduction to Matrices, providing more answers to your questions. We will introduce more complex operations such as Gaussian Elimination and Gauss-Jordan Elimination and demonstrate how to perform them. Learning these concepts will enable you to solve any nxn matrix.

## Determinants

In Determinants we introduce one of the most important properties regarding matrices -- how to control mankind! Just kidding. However, we will demonstrate some new methods for working with matrices. Using Determinants we will show how to solve matrices more easily and even determine if a matrix has a solution without having to solve them completely.

Concepts: 19
Quiz Points: 285

## N-Dimensional Vectors

Concepts: 19
Quiz Points: 285

### College Algebra

#### Try College for Free

Sophia online courses for college credit offers a faster path to earn your degree.