Math 175 Central, Transformations and Completing the Square

Reminder: In general, these activities are intended to either reinforce topics that were discussed during the past week or to prepare you for the topics that will be discussed during upcoming classes.

This week you will review (1) transformations, (2) completing the square, and (3) find a place to seek additional help with a few challenging problems.

Activity 1: This activity will allow you to practice (and hopefully better understand) graphing transformations.

The first web site contains a summary of graphing transformations. Once you read the page, click on the java applet link (near the top of the page) to bring up an interactive simulation. Click on each button in the list under the graph of the blue curve to see a translation (the red curves). You can move the translation by clicking on the graph itself. As you experiment with these transformations, try to think about which type of transformation gives the red curve shown; for example, determine if the red curve is more like f(x) + 2 or f(x+2), or some other transformation. To begin, click here.

There is an additional set of applets available on the web that allow you to study transformations. By moving the slider (small red dot) above each graph, you will see various transformations, and the value of the constant that is being changed to create the transformation. One kind of transformation that we did not cover in class, called horizontal scaling, is of the form f(kx) where the value k is some constant. Try to predict how the graph of f(kx) is related to the graph of f(x) by using the horizontal scaling simulation. What does f( .5 x) look like? What does f(2x) look like? To begin, click here.

When you complete the web activity survey (see below), you will be asked to identify graphs of transformations.

Activity 2: This activity will allow you to practice (and hopefully better understand) completing the square.

The website (click here) contains a good review of the steps to completing the square of a quadratic function. Once you have read the review, practice completing the square using the applet on this website.

When you fill confortable about completing the square, complete the web activity survey below.

Activity 3: Sometimes you may want a bit of extra guidance as you work through the homework. The solutions to the odd problems from an Applied Calculus text that is similar to ours are available on the web. We are making these problem sets available to you through the Guided Problems link (you can always find this link in Guided Problems Link under the Useful Links tab in the navigation menu on the left of this web page). Once you've downloaded a problem set and have worked out the solution to a problem, follow the link at the top of the guided problems page to visit the hotmath.org to find the solution to the problem. At this point, it would be helpful to work through many of the problems in Sections 1.1 to 1.4 of the guided problems. The password for hotmath.org is de34174ac . This service is similar to having a solutions manual to the problem sets, so use it as much as you need to throughout the semester. You do not need to turn these in for credit.

Once you have completed playing the games, studying transformations and completing the square, and have looked over the hotmation website, click on the Survey below and answer the questions (your responses will be sent to your instructor):

Transformations and Completing the Square Web Activity Survey