Graphing Piecewise Functions

Here are two websites that I have found that do a wonderful job of explaining how to graph piecewise functions.

The first shows boundaries and explains really well why the graph can't extend past the "fence."

The second uses Flash to show how part of each graph is removed.

Check them out if you are still confused!

Interactive Slope Activities for Mrs. Osterberg's Classes

1. Use rise over run to pass this quiz. http://www.algebrahelp.com/worksheets/check/graphing/slope.quiz

2. Find the slope of the line that goes through the following sets of points. Then check your answers here.

(0, 0) (1, 4)

(-3, 1) (5, 5)

(-1, 5) (6, 5)

(-1, 5) (7, 1)

(-3, 3) (1, -1)

(-4, 1) (2, -1)

(0, 1) (5, 2)

(0, 2) (5, 2)

3. Practice x and y intercepts as well as see examples worked here.

Solving Systems of Equations Using Gauss-Jordan Elimination

See this website for step by step direction and answers. Try it if you are stuck or if you have finished the problem to check your answer.

Polynomial Division: Long and Synthetic

Rather than explaining in lots of detail how to divide polynomials either using the long method or the synthetic method, I am sending my students to the following site. This PowerPoint is very brief, but it is very informative and shows every step of each process. Once the presentation is open, just press F5 to begin the slide show. A space bar or enter will move the slide show forward. The backspace key will back up if you need to see something again.

Simplifying Radical Expressions

My Algebra I students are having lots of problems with simplifying radical expressions. It seems that they have run across a concept that eludes them. I am posting about this topic to provide several more examples.

√18

First, we find the prime factorization of 18. If you need help with this concept, go here.

√18 = √(2•3•3)

Since the 3 is repeated twice, we can pull it out from under the square root symbol. Therefore,

√18 = 3√2

Now my students would be asking what happens if you have variables?

√24x³y²

√24x³y² = √(2•2•2•3•x•x•x•y•y)

Pull out everything that is repeated twice - 2, x, y. Leave everything else under the radical symbol.

2xy√(6x)

Some other places to visit for more details on this concept are here and here and here.

If you are one of my students and would like some extra credit, please visit those sites and comment here on whether or not they were helpful.

Solving Quadratic Equations

Here are a few sites that may help you when solving quadratic equations:

• by factoring
• by finding square roots
• by completing the square
• by Quadratic Formula
• by graphing
• extra examples

Solving Systems of Equations Using Elimination

I have found several websites that might help you with this concept.

Purple Math has a great site that shows examples here.

Check out the Unusual Outcomes in this PDF file. The other information there is also very good. The explanations are detailed.

Use this PDF file to help you determine when to add and when to multiply and then add.

Here are some problems that you can try to determine if you are getting it. Their answers are provided as well.