Solving Equations Graphically: TI–82 or TI–83
I. Solve Algebraically:
x3 – 2x = 0 ; x(x2 –2) = 0; x= 0, x2 – 2 =0;

II. Look at the graph of y = x3 – 2x in the window Xmin = –2, Xmax = 2,
xscl = 1, Ymin =–2, Ymax=2, yscl = 1.
III. Solve Graphically x3 – 2x = 0.
Observe that the graph crosses the x–axis three times. This means that there are 3

solutions
IV Find the solution between 1 and 2.
Procedure:
  1. Select the Calc menus. (2nd trace)
  2. Select (root)#2. See Left bound? (lower left of calculator screen)
  3. Move cursor to the left of the point of intersection with the x–axis
  4. Press enters. See Right bound? (Lower left)
  5. Move cursor to the right side of the point of intersection with the x–axis.
    You should see a set of double arrows at the top of the screen.
  6. Press Enter. See Guess?
  7. Move cursor to the point where the graph intersects the x–axis between 1 & 2.
    You should see, lower part of screen, x = 1.4142136 to seven decimal place.
    This means that 1.4142136 is a solution to 7 decimal places.
V. Repeat the above to find the solution between 1 and 2.
VI. View the graph of y = 2x5 – x4 – 4x3 + 2x2 – 30x + 15 in the window xMin = – 4,
xMax = 4, xscl = 1, Ymin =–80, yMax=80, yscl = 1.
  1. How many solutions are shown by the graph?
  2. Find all of the real solutions graphically.
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