Trace a function with the TI89 or with the TI Voyage 200

One of the important caracteristics of a graphing calculator is the possibility to trace mathematical functions. The Texas Instrument TI Voyage 200 and TI-89 graphing calculators can realize easily and quickly this operation. The TI Voyage 200 is particularly nice to use in reason of the good size of his screen.

To illustrate how to operate, we will take the example of a quadratic polynomial, knowing it is possible to trace any other sort of fonctions.

Remember

The function y=ax^2+bx+c represents the equation of a parabola. This parabola can meet the x axis in :
(A) 2 points with absciss x0 and x1. In that case the function can be represented with the form a(x-x0)(x-x1);
(B) 1 single point with absciss x0. In that case the function can be represented with the form a(x-x0)^2;
(C) none point;

Trace a function

We will take the function y=x^2+x-6=(x+3)(x-2) as example. Press the key "APP" on the graphics calculator. In the principal menu of the calculator, choose the equation editor "Y=Editor" then press the key "ENTER".

In the equation editor, type the formula of the function, that is x^2+x-6.

Press the key "F2" then 6 (Zoomstd), then ENTER.

The function trace himself immediately and automatically. You can easily see the points x0=-3 and x1=+2 where the curve intersects with the x axis.

Modify the scale of the display window

If you need to modify the scale of the display window of the function, use the keys "Lozenge" and "WINDOW".

By default, the window in which the function is traced has a layer with values -10 and +10 in x and y. Replace those values with -5 and +5 for instance. To write the minus sign, do not press the key "-" but the key "(-)". Don't forget to put a point "." at the end of the new values, otherwise the calculator will refuse to take in account those new values (xmin, xmax, ymin and ymax). Let the others values (xsc1, ysc1 and xres) unchanged.

Press the keys "Lozenges" then "GRAPH" and the function will be again immediately and automatically traced in the new window.