# 4.1: Graphing with the TI-84


We now use the TI-84 to graph functions such as the functions discussed in the previous chapters. We start by graphing the very well-known function $$y=x^2$$, which is of course a parabola. To graph $$y=x^2$$, we first have to enter the function. Press the $$\boxed {y =}$$ key to get to the function menu:

In the first line, enter the function $$y=x^2$$ by pressing the buttons $$\boxed {X,T,\theta ,n}$$ for the variable “$$x$$,” and then press the button $$\boxed {x^2}$$. We obtain

We now go to the graphing window by pressing the $$\boxed {\text{graph}}$$ key. We obtain:

Here, the viewing window is displayed in its initial and standard setting between $$-10$$ and $$10$$ on the $$x$$-axis, and between $$-10$$ and $$10$$ on the $$y$$-axis. These settings may be changed by pressing the $$\boxed {\text{window}}$$ or the $$\boxed {\text{zoom}}$$ keys. First, pressing $$\boxed {\text{window}}$$, we may change the scale by setting Xmin, Xmax, Ymin and Ymax to some new values using $$\boxed {\bigtriangledown }$$ and $$\boxed {\text{enter}}$$:

Note, that negative numbers have to be entered via $$\boxed {(-)}$$ and not using $$\boxed {-}$$.

## Note

The difference between $$\boxed {(-)}$$ and $$\boxed {-}$$ is that $$\boxed {(-)}$$ is used to denote negative numbers (such as $$-10$$), whereas $$\boxed {-}$$ is used to subtract two numbers (such as $$7-3$$).

## Note

A source for a common error occurs when the “Plot1" item in the function menu is highlighted. When graphing a function as above, always make sure that none of the “plots” are highlighted.

After changing the minimum and maximum $$x$$- and $$y$$-values of our window, we can see the result after pressing $$\boxed {\text{graph}}$$ again:

We may zoom in or out or put the setting back to the standard viewing size by pressing the $$\boxed {\text{zoom}}$$ key:

We may zoom in by pressing $$\boxed {2}$$, then choose a center in the graph where we want to focus (via the$$\boxed {\bigtriangleup }$$, $$\boxed {\bigtriangledown }$$, $$\boxed {\triangleleft }$$, $$\boxed {\triangleright }$$ keys), and confirm this with $$\boxed {\text{enter}}$$:

Similarly, we may also zoom out (pressing using $$\boxed {3}$$ in the zoom menu and choosing a center). Finally we can recover the original setting by using ZStandard in the zoom menu (press $$\boxed {6}$$).

We can graph more than one function in the same window, which we show next.

## Example $$\PageIndex{1}$$

Graph the equations $$y=\sqrt{7-x}$$ and $$y=x^3-2x^2-4$$ in the same window.

Solution

Enter the functions as Y1 and Y2 after pressing $$\boxed {y=}$$.

The graphs of both functions appear together in the graphing window:

Here, the square root symbol “$$\sqrt{\,\,}$$” is obtained using $$\boxed {2\text{nd}}$$ and $$\boxed {x^2}$$, and the third power via $$\boxed {\wedge}$$ and $$\boxed {3}$$ (followed by $$\boxed {\triangleright }$$ to continue entering the function on the base line).

## Example $$\PageIndex{2}$$

Graph the relation $$(x-3)^2+(y-5)^2=16$$.

Solution

Since the above expression is not solved for $$y$$, we cannot simply plug this into the calculator. Instead, we have to solve for $$y$$ first.

\begin{aligned} (x-3)^2+(y-5)^2=16 &\implies & (y-5)^2=16-(x-3)^2 \\ &\implies & y-5=\pm \sqrt{16-(x-3)^2} \\ &\implies & y=5\pm \sqrt{16-(x-3)^2} \end{aligned} \nonumber

Note, that there are two functions that we need to graph: $$y=5+\sqrt{16-(x-3)^2}$$ and $$y=5-\sqrt{16-(x-3)^2}$$. Entering these as Y1 and Y2 in the calculator gives the following function menu and graphing window:

The graph displays a circle of radius $$4$$ with a center at $$(3,5)$$. However, due to the current scaling, the graph looks more like an ellipse instead of a circle. We can remedy this by using the “zoom square” function; press $$\boxed {\text{zoom}}$$ $$\boxed {5}$$. This adjusts the axis to the same scale in the $$x$$- and the $$y$$-direction. We obtain the following graph:

## Note

We recall that the equation $$(x-h)^2+(y-k)^2=r^2$$ always forms a circle in the plane. Indeed, this equation describes a circle with center $$C(h,k)$$ and radius $$r$$.

This page titled 4.1: Graphing with the TI-84 is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Thomas Tradler and Holly Carley (New York City College of Technology at CUNY Academic Works) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.