# Calculator Notes for the TI-83 Plus and TI-84 Plus

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1 CHAPTER 3 Calculator Notes for the Note 3A Entering and Graphing Equations Equations are entered into the Y screen for various purposes, including graphing. You can enter up to ten equations, Y1 to Y0. Entering Equations Make sure you are in Function mode. Press MODE. In the fourth line select Func, then press Y. Enter an equation. The variable must be X using the X,T,,n key. You can edit an equation by using the arrow keys and DEL or 2nd [INS]. To remove an equation from the Y screen, highlight it and press CLEAR. Before actually graphing, you ll need to determine which part of the Graph screen you want to view. Setting the Window Press WINDOW and enter these values. Xmin the minimum x-value you want displayed. Xmax the maximum x-value you want displayed. Ymin the minimum y-value you want displayed. Ymax the maximum y-value you want displayed. Xscl and Yscl the number of units between tick marks on each axis. If there are too many tick marks, individual marks won t be distinguishable and the axes will appear too thick. Xres 1. Graphing Press GRAPH to see the graph of the equation(s). They will appear one after another, in the order listed on the Y screen. If the graph is not situated on the screen to your satisfaction, go back to the Window screen and change the values. Experiment with various window settings until you re satisfied with the appearance of the graph. You can turn off the graph of an equation without clearing it from the Y screen by arrowing to its symbol and pressing ENTER. When the symbol is not highlighted, the equation is turned off and will not graph. Discovering Advanced Algebra Calculator Notes for the Texas Instruments CHAPTER Key Curriculum Press

2 Note 3A Entering and Graphing Equations Tracing You can find approximate coordinates of points on the graph by tracing. Press TRACE and a spider appears on the first graph. Use the left and right arrow keys to move it along the graph. The coordinates of the spider s position appear at the bottom of the screen. You can move to the graphs of other equations by arrowing up or down. Notation on the upper-left part of the screen tells you which equation s graph is being traced. [0, 6, 1, 0, 12, 1] Zooming There are several ways to enlarge part of the graph. You can go back to the Window screen and change the window settings, or you can choose one of the commands that appear when you press ZOOM. 1:Zbox allows you to define your own enlargement. Select 1:Zbox to display a spider. Use the arrow keys to move the spider to the area you d like to enlarge. (This spider isn t restricted to the curve the way the trace spider is.) Press ENTER. Then draw a box by arrowing to the corner diagonally opposite from your current position. Press ENTER again. The interior of the box will enlarge and fill the screen. 2:Zoom In enlarges the screen by a factor of 4. Selecting 2:Zoom In will display a spider that you can position to where you want the center of your new enlarged screen. Press ENTER to see the new screen. 3:Zoom Out does the opposite of Zoom In. Select 3:Zoom Out, position the spider to the desired screen center, and press ENTER to see the new screen. Zooming automatically changes the settings on the Window screen. [0, 6, 1, 0, 12, 1] Graphing a Line and a Plot You can graph a line over a plot by entering the equation into the Y screen and the plot as directed in Note 1F. If you trace, arrowing up or down causes the spider to jump to each plot and to each function in order. [0, 6, 1, 0, 12, 1] 20 CHAPTER 3 Discovering Advanced Algebra Calculator Notes for the Texas Instruments

3 Note 3A Entering and Graphing Equations Setting the Graph Style In order to distinguish between several displayed graphs or to achieve a special effect, it is sometimes helpful to use a graph style other than the usual thin, solid line. Use the left arrow key to highlight the style symbol to the left of Y1 and repeatedly press ENTER to cycle through the various styles. These examples show the possible styles. Y1 graphs a curve using the usual thin, solid line. This is the default setting. Y2 graphs a curve using a thick, solid line. Y3 shades the area above the curve. [ 10, 10, 1, 10, 10, 1] Y4 shades the area below the curve. Y5 shows a moving circle that follows the curve and leaves a path. Y6 shows a moving circle that follows the curve but leaves no path (not shown on the screen here). Y7 graphs a curve using a dotted line. Note 3B Function Tables [ 10, 10, 1, 10, 10, 1] You can build a table of values for any function entered into the Y screen. Press 2nd [TBLSET]. TblStart the first x-value you wish to see in the table when first viewed. ΔTbl the difference between the x-values in the table. In the first screen here ΔTbl.1, so the difference between successive x-values is 0.1. ΔTbl can be negative. Indpnt: set to Auto means that the table will automatically start with the x-value equal to the TblStart value. If Indpnt: is set to Ask, the table will be blank until you provide the x-values. Depend: should always be set to Auto. Discovering Advanced Algebra Calculator Notes for the Texas Instruments CHAPTER 3 21

4 Note 3B Function Tables Press 2nd [TABLE] to display the table. If Indpnt: is set to Auto on the TABLE SETUP screen, you can arrow up or down to see more x-values. You can also arrow right to see values of other functions that are turned on in the Y screen. You can see only two columns of dependent variables at a time. If you arrow up to the top of a function column, you can see the equation displayed at the bottom of the screen. Press ENTER to edit the equation. The changes will be reflected in the table when you press ENTER again. Note 3C/App Balloon Blastoff Using the EasyData App You will need a CBR2 (Calculator-Based Ranger). Connect the CBR2 to the calculator. Press APPS and select EasyData. The CBR2 will immediately begin collecting distance data, which are displayed on your calculator screen. However, you need to collect data at shorter intervals for this experiment. Press Setup ( WINDOW ) and make sure 1:Dist is selected. The calculator will ask you to confirm, so press OK ( GRAPH ). Aim the CBR2 at the rocket and press Start ( ZOOM ). The CBR2 will collect data for about 5 seconds. If you want to stop it sooner, press the trigger. The calculator will display a graph of your data, which you can trace using the left and right arrow keys. If you need to redo the experiment, press Main ( TRACE ), then press Start ( ZOOM ). You will be told that this function will override the previous data. Press OK ( GRAPH ) and repeat the steps above. To end the application, press Main ( TRACE ), then press Quit ( GRAPH ). You will get a message telling you where the data are stored. Time data are in L1, distance data are in L6, velocity data are in L7, and acceleration data are in L8. 22 CHAPTER 3 Discovering Advanced Algebra Calculator Notes for the Texas Instruments

5 Note 3D Median-Median Line The calculator can find the equation of the median-median line for a set of data. Press STAT CALC 3:Med-Med, then enter the two lists that contain the data, separating them with a comma, and press ENTER. The independent variable list should be first. The command s default is to use lists L1 and L2, but it is a good habit to always specify the lists to be used. If you want the equation placed in Y1 on the Y screen, after the second list press, VARS Y-VARS 1:Function... 1:Y1 ENTER. Note 3E Residuals and the Root Mean Square Error [0, 5500, 500, 13, 19, 1] Once you have found a model for paired data, you can calculate the residuals and then the root mean square error. For this example, assume that your data are stored in lists L1 and L2 and your equation is stored in Y1. Residuals a. Press STAT ENTER. b. Move to the name cell at the top of list L3. Define list L3 as the residuals by entering the expression L2 Y1(L1). To get Y1, press VARS Y-VARS 1:Function 1:Y1. The resulting list will not change if you change the data in list L1 or list L2 or the equation in Y1. If you want this list to be dynamic (changing when list L1, list L2, or Y1 changes), enter the expression within quotation marks using ALPHA ["]. Discovering Advanced Algebra Calculator Notes for the Texas Instruments CHAPTER 3 23

6 Note 3E Residuals and the Root Mean Square Error Root Mean Square Error The root mean square error is defined as n y i ŷ i 2 i 1 s n 2 The numerator of the fraction is the sum of the squares of the residuals. The denominator is 2 less than the number of elements in list L3. a. First calculate the residuals in list L3 as described above. b. Calculate the numerator of the fraction and the value of n. Press STAT CALC 1:1-Var Stats 2nd [L3] ENTER. This puts the sum of the squares of the residuals into a variable called Σx 2 and the number of elements in the residual list into a variable called n. c. Enter this formula into the Home screen: 2nd [ ] VARS 5:Statistics:... Σ 2:Σx 2 ( VARS 5:Statistics 1:n 2 ) ) ENTER. The result is the root mean square error. For large values of n, you can find a good approximation by dividing n 1 instead of n 2. This is the sample standard deviation of the residuals, or the value of Sx when you do 1-Var Stats. Note 3F Greatest Integer Function To find the greatest integer less than or equal to a value, press MATH NUM 5:int(, enter the value, and then close the parentheses. If the value is a positive decimal number, the function truncates everything after the decimal point; if the value is a negative decimal number, it does the same and then subtracts 1. You can also use int( as a function of x. When graphing this function, the calculator may show almost-vertical segments that shouldn t be there. You can eliminate them by changing the graph style to a dotted line. (See Note 3A for help setting the graph style.) [ 4.7, 4.7, 1, 3.1, 3.1, 1] 24 CHAPTER 3 Discovering Advanced Algebra Calculator Notes for the Texas Instruments

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