A graphing calculator is an indispensable tool for high‑school courses such as algebra, precalculus, calculus, and trigonometry, and it’s also heavily used in science and engineering. The TI‑84 series from Texas Instruments is the industry standard, and the following instructions are based on that model. While most features carry over to other brands, be sure to consult your device’s manual for brand‑specific quirks.

The interface is divided into a display screen at the top and a keypad below. The keypad contains the usual numeric keys, but also offers a directional arrow set for navigating menus and a row of graph‑specific keys: Y= (enter a function), WINDOW (adjust axis limits), ZOOM (auto‑scale), TRACE (cursor control), and GRAPH (render the plot). Many keys have secondary functions; press 2ND or ALPHA to access them.

Graphing Functions

To plot a function, press Y= and type the equation in the form y=…. If your original equation isn’t solved for y (e.g., x + y = 5), rearrange it first (y = 5 – x). Use the X,T,θ,n key for the variable x, and the E key for exponents.

Set the viewing window: press WINDOW, then enter values for Xmin, Xmax, Ymin, and Ymax. Finally, press GRAPH to display the curve. Base models plot y in terms of x, but TI‑84 users can switch to x in terms of y via the STAT > EDIT > STAT PLOT menu and selecting the desired variable.

Linear Regression

Linear regression finds the best‑fit straight line (y = ax + b) through a set of data points.

1. Press STAT and choose EDIT (the default option). Enter your x values in column L1 and y values in L2, pressing ENTER after each entry.
2. Exit the edit screen by pressing 2ND + MODE (QUIT). The data are now saved.
3. Press STAT, navigate to CALC, and select LinReg… (ax+b). Use 2ND + 1 to load L1, comma, then 2ND + 2 to load L2. Press ENTER to compute.
4. To plot the scatter points, press 2ND + Y=, open the STAT PLOTS menu, enable Plot 1, set Xlist = L1, Ylist = L2, and choose Scatter. Press GRAPH to view the points.
5. Returning to the regression screen, the values for a and b appear; press GRAPH to overlay the best‑fit line.

Non‑Linear Regression

Non‑linear regression models curves such as exponential or logarithmic trends.

1. As with linear regression, use STAT > EDIT to load L1 (x) and L2 (y) and create a scatter plot via STAT PLOTS.
2. Identify the appropriate model (e.g., exponential, logarithmic). Then press STAT > CALC and select the matching regression option (e.g., ExpReg for exponential).
3. Set Xlist = L1, Ylist = L2, and scroll to StoreRegEQ. Use VARS > Y‑VARS to choose the target function (typically Y1).
4. Press ENTER to compute the regression equation, then GRAPH to superimpose the fitted curve over your scatter plot.

Solving Quadratic Equations

Quadratic expressions take the form ax² + bx + c = 0, where a ≠ 0. When graphed, they produce parabolas whose vertex indicates a maximum (if a < 0) or minimum (if a > 0).

1. Enter the quadratic as y = ax² + bx + c by pressing Y= and typing the expression with 2ND + Y= for zero.
2. Press GRAPH to display the parabola. Use ZOOM > Zoom > Zoom‑Fit if the shape is unclear.
3. To locate the vertex, press 2ND + TRACE to open the calculator’s “Calc” menu, select 2: Vertex, choose 1: Max/Min, and then ENTER. Adjust the left/right limits using the arrow keys and press ENTER again to display the vertex coordinates.
4. For x‑intercepts, return to the Calc menu, choose 1: Zero, set the search interval, and press ENTER to find the roots.