Zeros or roots of functions and solutions to equations can either be real or complex numbers. x-intercepts can only be real numbers.

The TI graphing calculator can be used to find the real roots of an equation.

- If your equation has something on the right side, subtract it from both sides so that the right hand side is 0.
- Go to Y=
- Enter the expression
- Hit Graph
- Change the viewing window if necessary so that you can see where the graph crosses the x-axis. You need to make sure that there is enough to the left and right of the x-intercept to select a point.
- Continue on to the specific steps for your calculator. If there is more than one x-intercept, you may need to change your viewing window and repeat the steps for each x-intercept.

- Press Calc (2
^{nd}Trace) - Choose Root (#2)
- For the Lower Bound, arrow to the left of the x-intercept and press enter.
- For the Upper Bound, arrow to the right of the x-intercept and press enter.
- For the Guess, arrow to the x-intercept and press enter.
- The TI-82 will return a value for x and 0 (or really close to it) for y.

For the TI-83, you may enter left bounds, right bounds, and guesses from the keyboard instead of arrowing and hitting enter. When it asks for a value, just enter your number and press enter.

- Press Calc (2
^{nd}Trace) - Choose Zero (#2)
- For the Left Bound, arrow to the left of the x-intercept and press enter.
- For the Right Bound, arrow to the right of the x-intercept and press enter.
- For the Guess, arrow to the x-intercept and press enter.
- The TI-83 will return a value for x and 0 (or really close to it) for y.

- Press Graph
- Press More and then Math (F1)
- Press Lower (F1). Arrow to the left of the x-intercept and press enter.
- Press Upper (F2). Arrow to the right of the x-intercept and press enter.
- Press Root (F3). Arrow to the x-intercept and press enter.
- The TI-85 will return a value for x and 0 (or really close to it) for y.

For the TI-89 and TI-92, you may enter lower bounds or upper bounds from the keyboard instead of arrowing and hitting enter. When it asks for a value, just enter your number and press enter.

- Press Math (F5)
- Choose Zero (#2)
- For the Lower Bound, arrow to the left of the x-intercept and press enter.
- For the Upper Bound, arrow to the right of the x-intercept and press enter.
- The TI-89 will return a value for x and 0 for y.

You do not need to supply a guess for the TI-89. You should make sure there is only one x-intercept in the interval specified or you won't know which one it is going to give you.

Find all real solutions to the equation exp(-x^{2}) =
-x.

**Note**: exp(x) is the exponential function and is often written
as e^{x}. It is e^{x} (2^{nd} LN) on the calculator,
but gets displayed as e^(x).

Begin by moving the -x to the left side where it becomes +x. The function
to graph is y_{1} = x + e^(-x^{2}).

Graph | Zero | Left | Right | Guess | Solution |
---|---|---|---|---|---|

The calculator says the solution is x = -0.6529186. The y-value of 0 is ignored. There was no y in the original problem.