A graphing calculator is a powerful instrument that does a lot more than merely add, subtract, multiply and divide numbers. These machines are, nowadays, not so much calculators as they are hand-held computers, similar to cell phones or tablets but with the specific purpose of helping you solve math problems, some of them quite complex.

Perhaps the most important of a graphing calculator's capabilities is its graphing tools. It is possible to both generate a graph given an equation or a set of data points, or use a provided graph to derive the equation and data associated with that graph.

The instructions here apply to TI-83 and TI-84 models, but non-Texas Instruments calculators operate in a very similar way.

Basic Graphing Functions

1. Press the "Y=" button to enter the function screen.
2. Enter the function (e.g., Y = X² - 4) into one of the lines.
3. Press "GRAPH." The calculator will draw the function for you.     

To find the Y-intercept of a graph that has been drawn:

1. Press "2nd," then "TRACE" to go to the "CALCULATE" window.
2. Highlight "value" and press "ENTER."
3. At the bottom of the screen that appears, enter "0" after "X=." The result will be the Y-intercept and associated X-coordinate.

Non-Linear and Linear Regressions

1. Press "2nd," and then "STAT PLOT." Press "ENTER."
2. After clearing all functions in "Y=", input data in L1 and L2.
3. Graph the data points by going to "9: ZOOM STat."
4. Look at "CALC" and choose a regression from the list.
5. Choose "9: ZoomSTat" to view data with a regression curve.
   

Quadratic Equations

1. Press the "Y=" button to enter the function screen.
2. Enter the function; for example, "−3x²+14x−8."
3. Press "2nd," then "TRACE" to go to the "CALCULATE" window.
4. Select whether the vertex is a maximum (as in this example) or a minimum.
5. Using the arrows, select the LEFT BOUND and the RIGHT BOUND to get the vertex coordinates.
6. Repeat the process to find the X-intercept or intercepts, if desired. It may be necessary to ZOOM out.