How to Do Everything We Need to Do on a TI Calculator in Algebra 2 for Now (Unless Davies Forgot Something)

Transcription

1 How to Do Everything We Need to Do on a TI Calculator in Algebra 2 for Now (Unless Davies Forgot Something) Before you do anything, set up your calculator so that it won t get in your way. Basics: 1. Press MODE and make sure all settings look like this. You can change them later as needed. IF AT ANY POINT YOU ARE STUCK IN A SCREEN YOU DON T WANT, PRESS 2 ND MODE WHICH IS QUIT. THIS SHOULD TAKE YOU OUT TO THE HOME SCREEN. All basic computation is done from the home screen. The image below shows a blank home screen. The Keys associated with graphing are across the top. 1. Click the y=. This takes you to a screen called the y editor. The y editor above has some equations in it and a plot on. Before you get started: Use the arrow keys to navigate and CLEAR all equations in your calculator (if there are any). Be sure to scroll below to Y 9 = and CLEAR anything that s there. If any plots are on (highlighted), use the arrow keys to navigate to them. You can turn Plots on or off by hitting the ENTER key while the selected Plot is flashing. The pic above shows the difference.

2 3. ZOOM is smack dab in the middle of your graphing keys. ZOOM 6 sets your graphing window to a standard default 20 x 20 window with the origin (0, 0) in the center. 4. STAT takes us to that special place where we can enter data into lists and then use it in a variety of ways. Press STAT 5 ENTER. This restores any lists that might be archived. Notice that above the 1, 2, 3, 4, 5, 6, keys you see L1, L2, L3, L4, L5, L6. These are lists that you can enter values into. Press 2 ND + 4 ENTER This will clear all of your lists out. If you have done this correctly, your calculator will say DONE on the home screen. STAT EDIT will take you to your lists where you can enter values. You can clear lists here as well by highlighting the list name (NOT THE FIRST ENTRY) and hitting CLEAR. By the way, if at any time you experience ERR: SYNTAX 1. Quit 2. Goto This means you have typed something incorrectly. Be sure to type every key as given including commas throughout this guided exploration.

3 5. As a last ditch resort, from the home screen you can completely reset your calculator defaults using 2 ND This will reset your defaults without erasing programs and apps. You can reset EVERYTHING using 2 ND THIS WILL CLEAR ALL YOUR PROGRAMS AND ANY ENTERED DATA OR EQUATIONS. 6. From the home screen go to the catalog by typing 2 nd 0 and scroll down to DiagnosticOn. (You can speed this up by typing ALPHA x -1 twice. This skips to the top of the D s). Type ENTER twice. You want this on in order to get the most information possible from your calculator. GRAPHING LINES Perhaps there are fancy calculators that will graph equations that aren t solved for y, but TI 83 and TI 84 plus requires that the equation be solved for y prior to graphing. The following sequence will take you through solving an equation for y, entering it into the y editor, setting the window as needed and using the technology to find y values. 1. Solve 2.3x 17.4y = 13.3 for y. 2. Put your equation into the y editor (type Y = to get there). Notice that you need the parenthesis and be careful not to confuse the (-) and the sign. The first is a negative for your calculator and the second is a minus or subtraction key. The x that we want is next to the ALPHA key. Y 1 = (-2.3x )/ Try ZOOM 6 4. Pretend you want to know what Y is when x is While still on the graph screen, hit TRACE. This allows you to travel along the line using the left and right arrows. The blinking cursor shows you where you are. At the top of the screen is the equation and at the bottom are the x and y coordinates for where you are. This is an image of a DIFFERENT equation that shows you a basic idea of what your screen should have.

4 Once you hit TRACE, you can type in a value for x and look at what the value for y is if your x value is in the window you are using. After you have hit TRACE and moved around on the line a bit, type 38.7 ENTER Your screen might say: ERR: INVALID 1. Quit 2. Goto This is because 38.7 is outside of the window range. Hit 2 ND MODE to quit and then hit WINDOW Your window setting looks like this after ZOOM 6 Since the Xmax of 10 is less than 38.7, your calculator gives you an error when trying to find the y value. Using your arrows, change the Xmax to Xmax = 50 and hit GRAPH TRACE 38.7 ENTER Now you should be able to see that Y = in the lower right corner. YAY! 5. Sometimes it s nice to look at values for your equation in table form. Let s try that right now. Isn t this fun everybody? Hit 2 ND GRAPH which takes you to the table. Hit 2 ND WINDOW Again, Davies lifted a pic of just any ole table off the image internet so it won t match yours but it gives you an idea of what to look for. You can scroll up and down using arrows and look at values in your table. Tables are useful if you know how to set them so that they show you what you want. This allows you to set up your table to see what you want. TblStart = 38.7 for example will start the table at 38.7 ΔTbl = 1 for example will make the x 1 unit apart. You can make this count by anything you d like. Experiment. For now, leave IndPnt: and Depend: on AUTO. Experiment with the window and table settings. Try to find the y intercept using both the TRACE and TABLE. Remember, the y intercept happens when x = 0. Solving for Intersection Points (Systems) using Intersect We will solve the following systems using technology. You should then solve it using substitution or elimination.

5 y = -2 +3(x 7) y = 10 5x 1. Type the system into the y editor and try ZOOM 6. Our intersection point is slightly below the screen. Go into the WINDOW and change Ymin to - 20 or so. Hit GRAPH (not ZOOM 6). You can use TRACE to estimate the intersection but it usually will be slightly off. 2. To get the closest (if not exact) solution, hit 2 nd TRACE 5 Again, your screen has different graphs, but should have x and y values at the bottom, a question about the first curve and an equation. a. Use the arrows left and right to get the blinking cursor as close to the intersection point as possible. This will be really important when we work with systems that have more than one intersection point like the one shown above. b. First curve? Is asking you what the first of the two equations is. It doesn t matter which of the two is First curve so hit ENTER c. Second curve? Is asking you what the second curve is. You should see that the equation at the top of the screen changed. Hit ENTER d. As long as you ve placed the cursor close to the intersection point, you need not guess so just hit ENTER again. Your calculator should have an output at the bottom that says Intersection X = Y = NOTE: If you have more than two equations in your y editor, it is important that you tell the calculator the correct First and Second curves. 3. Type the system s 1 = m and s 2 = m from problem 6 p.164 into your y editor and use the above step by step process to solve the system. 4. See if you can use the table to find when the spring lengths are 10 cm apart. Fun Facts

6 1. You can convert decimals to reduced fractions (when possible). Here is an example: Type 52/112 MATH ENTER ENTER to get 13/28. Now say you want to substitute that for x into y = 21.6x 19. Type 13/28 STO X ENTER (This stores 13/28 to X). Then type 21.6x 19 ENTER and you are given If you want the fraction version, type MATH ENTER ENTER and you get -314/ Look above the (-) key. Ans is where your calculator stores the most recent value that has been outputted to the screen. For example, clear your home screen then type (5) ENTER Your screen should say (5) -114 If you type 47(2 nd (-)) ENTER you will see 47(Ans) You calculator took the -114 stored it as Ans and multiplied it by To bring up previous lines that you have typed in, type 2 ND ENTER This is useful when doing the same calculation over and over as in some of the shifted sequences. Making Scatter Plots and Least Squares Regression Lines (LSRL) also Known as Lines of Best Fit BE SURE YOU RESET YOUR CALCULATOR USING THE PROCESS AT THE BEGINNING OF THE PACKET One of the major uses of linear equations is in the field of Statistics for creating prediction models. Below is a data table from your textbook p.150 and was actually taken from yet another textbook from way back in the day. The table gives the number of deaths caused by automobile accidents, D, per hundred thousand population in the U.S. for various years, t. t D Hit STAT ENTER 2. The first cell of L1 should be highlighted. Being typing the t values into L1. 3. Use the arrows to move to L2 and enter the values for D into L2. 4. Double check everything. Both lists should be the same length and look EXACTLY like the table above except vertical. 5. Hit 2 nd Y= Your screen should look something like this but all plots Off 6. Hit ENTER

7 Your screen needs to look like this just prior to graphing. Plot1 should be set to On, the Type should be the one that looks like a little scatter plot and you want to pull data from L1 for x and L2 for y. You can use arrows to navigate and ENTER to select On and the type of plot. Remember, your list labels are above the 1 through 6 keys. If your lists are not correct, change them. 7. Hit ZOOM 9 (Not ZOOM 6). This selects a window for your scatter plot so you don t have to. You can modify this window but it still has likely saved you time and hassle. You should see a scatter plot that isn t perfectly straight but is close. If your screen says: ERR: DIM MISMATCH 1: Quit Then you have a problem with the lists. Check and make sure that both are the same length and that you typed everything correctly. Check the STAT PLOT and make sure that you are pulling from the correct lists. The try again. If your screen says: ERR: INVALID 1. Quit 2. Goto There is a problem with what you are trying to graph. Check and make sure that there are no equations in your y editor and make sure you don t have another STAT PLOT on. Your calculator could be trying to fit things on the screen that just don t go together. 8. The Least Squares Regression Line is the one and only line of best fit. Though the ones that you find by eye are very good, it is virtually impossible to guess the LSRL. Let s have TI do it for us. Hit STAT and use the right arrow to go to CALC BOTH options 4 and 8 do the exact same thing. Type 4 If your calculator is older (like Ms. Davies) you will see LinReg(ax + b) Type 2 ND 1, 2 ND 2 and your screen should read LinReg(ax + b) L1, L2 NOTE: the comma is above the 7 key If your calculator is younger, you might see something like this:

8 Assuming you have used lists 1 and 2 for your data, your information should be filled out as you see it. It is only necessary for you to fill in the Xlist and Ylist. The others can stay blank. The screen to the left is set up to put the equation into Y 1 in your Y editor which is actually pretty neat. Your calculator should have given you: LinReg y = ax + b a = b = r 2 = r = If you don t have the r values, go back to the start-up pages and turn on your diagnostic. 9. Your equation is stored for you whenever you calculate one. To paste it into your y editor, go to Y 1 = and type VARS 5 use the right arrow to get to EQ and hit ENTER Your equation should be pasted in Y 1 and ready to graph. So, what are you waiting for? Hit GRAPH then say in an enthusiastic voice Oh, that is so totally cool! Now, your task is to work #8 on page 164. Type the data into lists, make a scatter plot, sketch the plot, find the line of best fit (LSRL) using your calculator and decide if it is a reasonable predictor. If not, choose a part of the data set that might produce a more reasonable model and do it all again. It will be such fun!