Introduction to the Graphing Calculator for the TI-86

Transcription

1 Algebra 090 ~ Lecture Introduction to the Graphing Calculator for the TI-86 Copyright 1996 Sally J. Glover All Rights Reserved Grab your calculator and follow along. Note: BOLD FACE are used for calculator steps. BOLD UNDERLINED are actually keys and NOT-UNDERLINED BOLD are soft keys (keys that show-up on the screen in menus). Problem 1: Graph y = 5x 2 using window x[-5,5], y[-5,5]. Find the exact y-axis intercept point. Trace to find the approximate x-axis intercept point with coordinates accurate to the nearest tenth. Hit: GRAPH y(x)= At this point your calculator should ask you for the equation by showing y1= on the screen. If it has y2 or y3 or there is already an equation in there, hit DELf until it says y1= only. Type in the equation: 5 x - 2 Note: for x you can either use the soft key x or x-var. Hit EXIT to remove the lower menu from the screen so you can hit WIND (on the 86) or RANGE (on the 85). This area is your viewing window set-up. We want xmin=-5, xmax=5, xscl=1, ymin=-5, ymax=5, yscl=1, and xres=1 (on the 86 only). (Scl sets the scale, i.e., we are making each tick mark on each axes 1 and Res is resolution which can always be left at 1.) Now hit GRAPH. (Note: this is the GRAPH on the screen not the graph key!) You should get a straight line passing through quadrants III, IV, and I that looks like this:

2 Now we are going to locate the exact y-intercept point. Hit TRACE. The blinking cursor should have automatically gone to the y-intercept point. Note that the coordinates are given at the bottom of the screen. The exact y-intercept point is (0, ). (Note: if the cursor did not automatically jump to the y-intercept point, type 0 ENTER while in TRACE.) Answer: The exact y-intercept point it (0,-2). Now we are going to locate the approximate x-intercept point. While still in TRACE use your left and right arrows (not up and down arrows) to move the blinking cursor to as close to the point where the line crosses the x-axis as possible. To the nearest tenth the x- intercept point is approximately (,0). (Note: we will learn a more accurate way to find the x-intercept point in a moment.) Answer: The x-intercept point is approximately (0.4,0). ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Problem 2: Graph y = 4 5x 2 using window x[-5,5], y[-5,5]. Trace to find the approximate local minimum point with coordinates accurate to the nearest hundredth. Find the exact y-axis intercept point. Find the exact point on the graph where x=1.6. Find the exact x-axis intercept points using ROOT. If your graphing menu is not already displayed on the screen, hit GRAPH. Hit y(x)= then DELf to clear the old equation then type in the new one. The absolute value function abs is in your 2 nd math number menu so hit 2 nd MATH NUM abs ( 4 5 x ) 2 followed by EXIT GRAPH to graph the equation. You should get a V-shaped graph that looks like this:

3 Now we are going to locate the approximate local minimum point. Hit TRACE. Use your left and right arrows to move the blinking cursor to as close to the local minimum point (the bottom of the V-shape) as possible. With coordinates to the nearest hundredth the local minimum point is (, ). Answer: The local minimum point is approximately (0.79,-1.97). (Answers close to this are acceptable.) Now we are going to locate the exact y-intercept point. While still in trace, type 0 ENTER. This will force the cursor to move to the point where x=0 (which of course is the y-intercept point). The exact y-intercept point is (0, ). Answer: The exact y-intercept point is (0,2). Now we are going to locate the exact point on the graph where x=1.6. While still in trace, type 1.6 ENTER. This will force the cursor to move to the point where x=1.6. Read the corresponding y-coordinate off the bottom of your screen. The exact point is (1.6, ). (Note that you can verify this algebraically by substituting 1.6 into the original equation for x and solving for y. Try it, do you get the same result?) Answer: The exact point is (1.6,2). Now we are going to locate the exact x-intercept points using ROOT. This graph has two x-intercept points. Let s find the leftmost one first. With the graphing menu displayed on the screen, hit MORE MATH ROOT. The calculator will ask, Left Bound?. Use the left/right arrows to move the cursor along the curve until it is a little to the left of the leftmost x-intercept point and hit ENTER. The calculator will ask, Right Bound?. Use the left/right arrows to move the cursor along the curve until it is a little to the right of the leftmost x-intercept point and hit ENTER. The calculator will ask, Guess?. Use the left/right arrows to move the cursor along the curve until it is close to the leftmost x-intercept point and hit ENTER. The calculator should now find the x-intercept point (the root of the equation) and display its coordinates. The exact leftmost x-intercept point is (,0).

4 Answer: The exact leftmost x-intercept point is (0.4,0). Let s find the rightmost x-intercept point. Press EXIT or GRAPH to get the graphing menu re-displayed on the screen, then hit MORE MATH ROOT. The calculator will ask, Left Bound?. Use the left/right arrows to move the cursor along the curve until it is a little to the left of the rightmost x-intercept point and hit ENTER. The calculator will ask, Right Bound?. Use the left/right arrows to move the cursor along the curve until it is a little to the right of the rightmost x-intercept point and hit ENTER. The calculator will ask, Guess?. Use the left/right arrows to move the cursor along the curve until it is close to the rightmost x-intercept point and hit ENTER. The calculator should now find the x-intercept point and display its coordinates. The exact rightmost x-intercept point is (,0). Answer: The exact rightmost x-intercept point is (1.2,0). Using ROOT to find exact x-intercept points is VERY IMPORTANT! ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 3 2 Problem 3: Graph y = 2x + 3x 9x 10. Trace to find the approximate local minimum point with coordinates accurate to the nearest hundredth. Produce the graph on your own now. The problem is that you can t see the whole graph, right? So we need to change the viewing window. We need to see lower on the graph so we can see the local minimum point. So we need to change the ymin value of our window settings. Hit WIND (or RANGE on the 85) and change the viewing window so that ymin=-20. Regraph to see the whole picture! It should look like this:

5 Now trace to find the local minimum point (the bottom of the valley that is in quadrant IV). With coordinates to the nearest hundredth the local minimum point is (, ). Answer: The local minimum point is approximately (0.82,-14.26). (Answers close to this are acceptable.) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Problem 4: Change your viewing window back to y[-5,5] and then graph How many x-intercepts does it have? y = 200x 50x + 3x Wow, it is hard to tell how many x-intercept points this graph has. We will have to zoom in to see. There are several options in the zoom menu, but the one that gives you the most control is zoom box. Hit ZOOM BOX. Use your arrows (all four of them if necessary) to move the cursor into quadrant II. You want to establish the northwest corner of your box which will surround the origin area into which we would like to zoom. When you are satisfied with the placement of this corner, hit ENTER. The cursor will change shape to a little flashing square. Next, use your arrow to move the cursor into quadrant IV. See how the little box forms surrounding the origin area of the graph?

6 When you are satisfied with the placement of this southeast corner of your box, hit ENTER. The curve will regraph automatically zoomed into that boxed region. Can you see how many x-intercepts the graph has now? No not yet? You may need to zoom box several times to be sure! Go for it!! Eventually you will be able to answer the question: This graph has (how many?) x-intercept points. Your graph should look something like this: Answer: This graph has three x-intercept points. BTW, after zooming and/or altering your window it is strongly advised that you reset your window to the standard settings. The easiest way to do this is to hit ZOOM STD. (That is zoom standard nothing to do with sexually transmitted diseases!) Now try these examples again on your own referring to this sheet as necessary. Then try graphing some equations from your text. Have fun!