Texas Instruments TI-92 Getting Started page 19

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Graphing Technology Guide: TI-92
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Figure 5.55: A zero of y = x – 8x
TRACE and ZOOM are especially important for locating the intersection points of two graphs, say the graphs of y =
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–x + 4x and y = –.25x. Trace along one of the graphs until you arrive close to an intersection point. Then press or
to jump to the other graph. Notice that the x-coordinate does not change, but the y-coordinate is likely to be
different (Figures 5.56 and 5.57).
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Figure 5.56: Trace on y = –x + 4x Figure 5.57: Trace on y = –.25x
When the two y-coordinates are as close as they can get, you have come as close as you now can to the point of
intersection. So zoom in around the intersection point, then trace again until the two y-coordinates are as close as
possible. Continue this process until you have located the point of intersection with as much accuracy as necessary.
You can also find the point of intersection of two graphs by pressing F5[Math] 5[Intersection]. Trace with the
cursor first along one graph near the intersection and press ENTER; then trace with the cursor along the other graph
and press ENTER. Marks + are placed on the graphs at these points. Then set lower and upper bounds for the x-
coordinate of the intersection point and press ENTER again. Coordinates of the intersection will be displayed at the
bottom of the window (Figure 5.58).
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Figure 5.58: An intersection of y = –x + 4x and y = –.25x
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5.3.2 Solving Equations by Graphing: Suppose you need to solve the equation 24x – 36x + 17 = 0. First graph y =
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24x – 36x + 17 in a window large enough to exhibit all its x-intercepts, corresponding to all the equation's zeros
(roots). Then use trace and zoom, or the TI-92's zero finder, to locate each one. In fact, this equation has just one
solution, approximately x = –1.414.
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