This applet will enable you to learn synthetic division with ease and efficiency. Polynomials of up to degree 6 can be entered, the program will do the arithmetic, you need to learn how to do this on your own. Have fun!![br][br]When entering coefficients, make sure that you first arrange the terms in descending order of the powers. Use a 0 as a placeholder when the coefficient of a term is missing. Your last coefficient is a constant term, even if it is a 0. If your polynomial has degree 5 or less, leave the last box(es) blank or you can use the line for that polynomial function. If your polynomial has degree 2, the quadratic formula or factoring will be more efficient.[br][br]To preserve the formulae in the cells, be sure to type only in the blue or pink boxes. A Reset button will allow you to start an new expression. Use the [b]Reset[/b] button on the graphic screen restore formulae in spreadsheet. Sample1 show a fully factorisable expression; Sample2 shows a partially factorisable expression.[br][br][b]Warning[/b]: This applet does not solve all Synthetic Division problems, it is a tool to help you to learn to do synthetic division yourself.

This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers as a worksheet to be completed for a grade.

In this activity you will use a slider to change the basic (parent) functions. You will be able to change value of the sliders [math]a_0[/math], [math]a_i[/math], h, and k to transform the function by moving these sliders. The [math]r_0[/math] and [math]r_i[/math] allow your to reflect outside and inside of the function change you results. There are two check boxes to permit the user to easily demonstrate the results of a vertical or horizontal line test. The [math]a_0[/math] and the [math]a_i[/math] represent the effects of multipliers outside of the function f(x) and inside the parenthesis of f(x), sometimes these multipliers when used separately produce the same graph. When [math]a_0[/math] or [math]a_i[/math] are zero, the resulting graph is a constant function.[br] 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[/img] [br][[b]Note[/b]: you may need to move a panel right to about 10 on x-axis.]

Your job is to determine the effects of each of the sliders on parent functions.[br]a) What does [math]a_o[/math] do to each function? Hint: its effects are the same for all functions.[br]b) What does [math]a_i[/math] do to each function?[br]c) What does h do in each function?[br]d) What does k do in each function?[br]e) What does [math]r_o[/math] do in each function?[br]f) What does [math]r_i[/math] do in each function?[br]g) Which axis is effected by the [color=#1551b5]blue[/color] sliders?[br]h) Which axis is effected by the [color=#c51414]red[/color] sliders?[br][br]Use these handouts as a guide to analyze the included functions.[br][br] Student worksheet (Original) [url=http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/documents/Transformations_Families_of_Functions_Student.pdf]PDF[/url] [url=http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/documents/Transformations_Families_of_Functions_Student.docx]DOCX[/url] [url=http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/documents/Transformations_Families_of_Functions_Student.doc]DOC[/url].[br] Graph sketching guideline worksheets [url=http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/documents/Graphing%20templateAlg2.pdf]Algebra II/Regular Precalculus[/url] [url=http://web.psjaisd.us/auston.cron/ABCronPortal/GeoGebraMenu/GeogebraFiles/funcProps/documents/Graphing%20templatePreCal.pdf]PreCalculs/Calculus[/url] (two templates per page)[br] New worksheet in process of completion[br][br]This applet can be used by teachers in a demonstration mode in the classroom or teachers can have students load it on their own computers as a worksheet to be completed for a grade.