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How do i input the equation f(x)= x^3 -3x+2 (-2,2). I need to graph and fine the local maximum and minimum

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I am puzzled by the (-2,2) after the equation. I suspect it is the coordinates of some point. But I won't push the matter further, and I will just ignore that info. I am no mind reader.

  1. Turn calculator ON.
  2. If you do not see icons, press Menu.
  3. Use navigational arrows to highlight [GRAPH] and press [EXE]
  4. Type the function.
  5. Use the [X.T,theta] key below [ALPHA] to type the X variable or the [ALPHA][+]. In general you should use the [X,T,theta] because is context sensitive: If you draw parametric or polar graphs, pressing that key gives you the right variable (T, or theta)
  6. Use the caret [^] 3 to raise X to the third power and complete the function. and press [EXE]
  7. At the bottom of the screen you see some tabs.
  8. Press [F3:Type] and you will see all types of graphs you can draw. But since you want Y=, press [EXIT] to return to Y=editor
  9. Press the Function key to above which you see [DRAW]
  10. Adjust the Window dimensions if necessary
Finding the min and max
  • While the graph is still displayed press [SHIFT][F5:G-Solve].You see all the possible calculationsF1:root, F2:Max,F3:Min,F4:YiCPT (y_intercept),F5:Isct (intersection) F6:=> to show the others, among which is the F3:integral.
  • Press F3:min and hold your breath.
  • After a while you get your minimun. Be patient, even if the small square at the top right disappears.
  • Once you get the minimum, press [SHIFT][F5-G-Solve] and repeat for the maximum.

Posted on Feb 01, 2010


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How i can solve quadratic equations which have no real roots

If the quadratic equation has no roots, you cannot find the roots. The discriminate is negative, so if we attempt to use the quadratic equation, we get no roots.

For example, y=x^2 +0x + 3

a=1, b=0, c=3

(-b+/- sqrt(b^2 -4ac))/2a

Substituting in the numbers, we get

x= (-0 +/-sqrt(0^2 - 4(1)3))/2
x= (0 +/- sqrt (-12))/2

We cannot do the square root of -12. Therefore, there are no roots. This is the same as having no x-intercepts. The discriminant is b^2-4ac. In this case it is -12. Thus, there are no real roots.

However, you can still determine the maximum or minimum, the vertex, the axis of symmetry, the y-intercept and the stretch/compression. With this information you can graph the equation.

In this case, the y-intercept is 3, the vertex is at (0,3), the axis of symmetry is x=0, the minimum value of the function is 3.

Good luck.

Let me know if you have any questions.


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While your TI-83 plus cannot explicitly find increasing or decreasing intervals, it can find the minimum(s) and maximum(s) of a function.
Press the "Y=" button.
Enter the equation in "y=" format into the first open equation.
Press the "GRAPH" key.
If the maximum and minimum of the curve are not shown in the window it has, press ZOOM->0.
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My TI-83 Plus calculator won't graph anything whatsoever. Did I need new software. Please help me.

First - Are you graphing within the proper window? Hit the zoom button and change it to zoom Standard within the graphing window.

Second - Are you inputting the equation correctly? Make sure you are inputting your equations in a y= format. If possible, please reply with a screenshot of your graph screen.

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The actual graph depends on the constants (parameters) that are in the equation. Try playing with the dimensions of the window by zooming in or zooming out.
The most interesting part of the graph is the region near the maximum or minimum.
Here is a graph of the function y=X^2-5X 13 when drawn with standard window dimensions
Not very revealing. However if you press the Zoom key and select [2:ZoomIn] you see this (no changes) but the calculator is ready to accept your input concerning the new center of the graph.
At this stage, use the Arrow keys to move the center of the graph to another point as in the next screen capture.

Notice the new center as a sign on the screen and its coordinates at the bottom. By pressing [ENTER] you get this
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