# October 2010 Archives

## Algebra 1 - Solving Rational Equations

After working with multiplying and dividing both rational expressions and polynomials, today's free Algebra 1 video may feel like a much-earned break. Today's video is on Solving Rational Equations and I love it because we're actually finding an answer that we can then go back and check for accuracy! Anytime you can check your answers is a good thing in my eyes. If you make a mistake you'll know it and be able to figure out what you did wrong, which helps you ace both homework assignments and tests. You'll learn how to solve rational equations by using cross products, and then how to solve rational equations using the lowest common denominator. Professor Edward Burger shows the relevancy of this math concept with a real-world application and ends on a lecture about identifying extraneous solutions. Today's video has a total of 4 lectures on it, so make sure you click the forward button to the left of the time stamp to move to the next lecture on the video!

As this video is the last of the Algebra 1 course, it's a good time to remind you all about our math placement tests. If you aren't sure which course in our curriculum sequence is the best place to start, take a stab at our free and easy to use placement tests. They'll help you so you don't accidentally buy a course that's either way too easy or way too hard.

Have a great weekend!

## Algebra 1 - Dividing Polynomials

In Algebra, rational expressions and polynomials can be tricky. We've learned that multiplying and dividing rational expressions is not nearly as bad as it seems in a past video. Now it's time to delve deeper into Dividing Polynomials in today's free Algebra 1 video. You'll see there's nothing to dividing a polynomial by a monomial. Then, Professor Burger ratchets up the difficulty with dividing a polynomial by a binomial and then even further when we jump into polynomial long division. Sound intimidating? Don't get overwhelmed, as these lectures will teach you everything you need to know! You'll find it much more pleasing to learn from a video than a textbook and I bet by the end of the 5 lectures, dividing polynomials will be a breeze. Just make sure you click the forward button to the left of the time stamp to move to the next lecture so you don't miss a minute.

## Algebra 1 - Multiplying and Dividing Rational Expressions

While the thought of multiplying and dividing rational expressions may have you quivering in your shoes, it's not nearly as hard as it looks. If you need a little help, want to review this concept, or just sample our online lectures, check out today's free Algebra 1 video on Multiplying and Dividing Rational Expressions. In addition to learning how to multiply and divide rational expressions, you'll also learn about simplifying complex fractions. Complex fractions contain one or more fractions in the numerator, the denominator, or both. Our math professor, Edward Burger, is an award-winning teacher who loves math so much he wants to share it with the rest of the world. What this results in is a fun lecture that will keep you awake instead of nodding off at your desk. He also makes sure to give you real world examples so you know how this could be used outside of the classroom.

Most folks would prefer to learn from a video than a text book and we think you'll agree!  Just remember that what you are seeing is just one part of our online curriculum. When you sign up for one of our courses, you'll also get a lesson plan, interactive exercises, worksheets, and tests.

Don't forget that today's video has a total of 6 lectures! You'll need to hit the forward button to the left of the timestamp to move to the next lecture on the video.

## Algebra 1 - Rational Functions and Expressions Worksheet

If you followed us this week, you've seen the free videos on Rational Functions and Simplifying Rational Expressions. Today it's time to test how much of that knowledge you retained as we're sharing a free Algebra 1 worksheet. Get ready to identify excluded values and asymptotes, graph rational functions, and simplify rational expressions. All of our courses come with worksheets for both each topic and then each subchapter. Today's free worksheet is a subchapter worksheet with 4 pages of questions to help cement the concepts you just learned. Of course, if you purchase one of our courses, you'll also enjoy a full dashboard around the video, notes, animations, automatically graded exercises, lesson plans and tests.

## Algebra 1 - Simplifying Rational Expressions

Are you ready for today's free Algebra 1 video? Watch with Professor Burger as he lectures on Simplifying Rational Expressions. A rational expression is an algebraic expression whose numerator and denominator are polynomials. Of course, in rational expressions the denominator cannot equal 0, so you'll learn how to find any excluded values of the rational expression first. Then as you progress to more difficult problems, Professor Burger will cover simplifying rational expressions using opposite binomials. Whew! That's a mouth full! While these can be a bit trickier, you'll have no problem understanding how to do this after watching today's lectures. If you've ever wondered about practical uses of rational expressions, we have a real world example in the last lecture. Today's video has a total of 5 lectures to get you up to speed on simplifying rational expressions. Just make sure you click the forward button to the left of the time stamp to move to the next lectures on the video.

And don't forget to follow us on Twitter and Facebook! We love talking with our students and their families. We're always posting great links and free resources for our followers, so come join us and our great online community of homeschoolers, independent students, and even public schoolers!

## Algebra 1 - Rational Functions

A rational function is a function whose rule is a quotient of polynomials in which the denominator has a degree of at least 1.  Today's free Algebra 1 video covers Rational Functions over 4 lectures with the wonderful Professor Edward Burger. In today's video you'll be identifying excluded values, which are values of x that make the function value y undefined in any function involving both x and y.  Then you'll jump to graphing rational functions when Professor Burger teaches about identifying asymptotes. An asymptote is a line that a graph gets closer to as the absolute value of a variable increases. To graph a rational function, you need to find the vertical and horizontal asymptote. And finally, in the very last lesson, Professor Burger will demonstrate a real world use of rational functions: cutting diamonds! Who knew that math was used in maximizing the brilliance of diamonds!? Watch all 4 lectures to get a great overview of rational functions. Just don't forget to click on the forward button to the left of the time stamp to move to the next lecture.

Have you seen our math placement tests? It can be difficult deciding what course best suits your student. So stop guessing and instead use our free placement tests! They'll help you determine your student's skill level and where in our curriculum sequence they belong.

## Algebra 1 - Multiplying and Dividing Radical Expressions

Radical expressions can be some of the most intimidating math problems to encounter. This is especially true when you start multiplying and dividing square roots. What looks scary and difficult can in fact be simple and for some, fun. Professor Edward Burger will run through several difficult-looking problems in today's free Algebra 1 video on Multiplying and Dividing Radical Expressions. Our good friend FOIL returns as we learn more on how to simplify radical expressions. We're also diving into simplifying a fraction containing square roots which will involve rationalizing the denominator. Rationalizing the denominator is the process of simplifying a quotient containing a square root in the denominator by multiplying by a form of 1 in order to get a perfect square radicand in the denominator. With 4 lectures to learn from, you'll become fearless when it comes to multiplying and dividing radical expressions. Just make sure you click the forward button to the left of the time stamp to move to the next lecture on the video.

Don't forget about our Video Biology app! Just in time for the school year, we've released a free app that gives you access to our biology videos no matter where you are! The free app comes with 10 free videos. However, if you want to be able to view any of the over 300 lectures we have for Biology, you can pay a small fee for monthly access. This way you only have to pay for a few months to help you get through that biology course. Or maybe you want to test out our curriculum and see what our lectures are like. This is an inexpensive way to do just that. Just remember, when you do sign up for a full course with us, you not only get the video lectures, but a full dashboard, worksheets, tests, and interactive exercises to help you get your Biology on!

## Algebra 1 - Radical Expressions

A radical expression is an expression that contains a radical symbol (âˆš). The expression under the radical symbol is called the radicand. While basic square roots aren't too terribly difficult, the idea of simplifying a square root with a quadratic equation might have many students running away out of fear. Worry not, because Professor Edward Burger has you covered in today's free Algebra 1 video on Radical Expressions. He'll demonstrate just how simple it can be to handle such difficult expressions.  After watching all 5 lectures on today's video, you'll be using properties of square roots to simplify radical expressions where the radicand is a non-perfect square, a fraction, or an algebraic expression. So, check out today's video and make sure you click the forward button to the left of the time stamp to move to the next lecture so you catch them all!

## Algebra 1 - Linear, Quadratic, and Exponential Models

With all the different types of functions you learn in Algebra 1, it is interesting that you can often look at a graph of data and make a prediction about what type of function it is. For example, we know that a quadratic function's graph will always be a parabola and a linear function will always be a straight line. You can also look at the data set and learn quite a bit about the function. The differences between the dependent variables will determine which type of function you are looking at. In today's free Algebra 1 video, Professor Edward Burger covers Linear, Quadratic, and Exponential Models. Over three lectures he'll show you the power of looking at data, finding patterns, seeing a potential model, and once you have the model, extrapolating into the future. Just make sure you click the forward button directly to the left of the timestamp to jump to the next lecture on the video.

## Algebra 1 - Exponential Functions

An exponential function is a function where the unknown is appearing in the exponent. The form is f(x)=abx, where aâ‰ 0 , bâ‰ 1 and b>0.  Basically, they are used to show instances when a constant change in the independent variable gives the same proportional change in the dependent variable. In today's free Algebra 1 video on Exponential Functions, you'll see several real world examples to teach this concept because often these functions are used to model real world things. Find out how you can utilize exponential functions to determine the squirrel population in 5 years! You will also learn how to determine if a set of ordered pairs satisfies an exponential function and how to identify and graph an exponential function. Make sure you click on the forward button to the left of the timestamp to move to the next lecture, because there are a total of 6 lectures on today's video.

Professor Burger was just recently featured in an article in The Chronicle of Higher Education. We are excited that they did a profile on him and his love of teaching math. Even if you feel you know all about Edward Burger, you should read this article, as there are all sorts of interesting facts about his path into teaching. It's an inspiring article that makes me wish I could have taken one of his math classes in college.

## Algebra 1 - Geometric Sequences

When we have a collection of numbers that come together in a certain order, it's called a sequence. A geometric sequence is a sequence where there is a common ratio that allows us to generate the sequence by taking one term and multiplying it by the common ratio to get the next term. How do you determine if a sequence is a geometric sequence? Watch today's free Algebra 1 video on Geometric Sequences to find out. Professor Burger will not only demonstrate how to figure if a sequence is geometric or not, but he'll also show you how to find a future term in a geometric sequence. You'll gain a strong understanding of the concept with multiple sample problems and even a real world example of how you might bump into geometric sequences in your life. Just don't forget to click on the forward button to the left of the time stamp to move to the next lecture. You don't want to miss a second of Professor Burger's lectures.

## Algebra 1 - Transforming Quadratic Functions

Continuing our studies in Quadratic Functions, today we're going to delve deeper into graphs and how to determine what the parabola will look like based upon the function. In today's free Algebra 1 video on Transforming Quadratic Functions, Professor Burger will show you how you can start with the basic quadratic and change the formula a bit, which in turn moves the graph around. Discover how one number can make the parabola either wider or narrower through several examples. It's simple once you learn and, of course, easily testable by inputting values into the function. As we're graphing so much, there's a lecture in today's video that shows you how to utilize a graphing calculator, a very useful tool moving forward in your math studies. There are 3 lectures today, so make certain you click on the forward button directly to the left of the time stamp to move forward and view them all.

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