Graphically find a root of

between **x=0** and **x=1** which is accurate to within **0.00001**
using the TI-85 graphing calculator.

[Press here to see animation again!]

- If you are not familiar with the graphing of functions on the TI-85, then first read the Initial Setup page from Little's Basic Guide to the TI-85.
- Press the GRAPH key and then pick
**y(x)=**by pressing the F1 key. - If necessary, keep pressing F4 key until only
**y1=**appears on the screen. - Type in
**cos x - x^2**and press the ENTER key.

- The range settings for the graph above is
**[0, 1]**×**[-1, 1]**: - Pick
**ZOOM**by pressing the F3 key. - Press the MORE key twice so that
**ZFACT**appears on the menu. - Press the F1 key to pick
**ZFACT**. - Since we want the answer to be accurate to within
**0.00001**, we want to zoom in quickly. We enter**10**at each of the prompts**xFact**and**yFact**followed by the ENTER key. With these settings, the zooming in will be at a factor of**1/10**. Since we started with an interval of length**1**, the length of the interval after one zooming in is**0.1**; after two zooming in's, the length is**0.01**, etc. - Pick
**ZOOM**by pressing the F3 key again. - This time pick
**ZIN**by pressing the F2 key. - You will now see a flashing tick mark in the middle of the screen and
the coordinates of the tick mark at the bottom of the screen:
- Using the arrow keys, move the tick mark as close to the intersection of the
graph with the horizontal line (which is the
**x**-axis) as possible and press the ENTER key. - Repeat the latter step at least six times.
- Press the EXIT key followed by the F2 key to pick
**RANGE**. The following screen was obtained:after seven zooming in's. This indicates that the root is between

**0.824132251587**and**0.824132351587**;**0.824132**satsifies the desired accuracy.A more efficient way to find the root with the TI-85 graphing calculator is to use the SOLVER key.