# A Lesson on Graphing Equations Using the Graphing Calculator

This article outlines a lesson plan in which students are shown how to use a graphing calculator to solve linear and quadratic equations.

## Overview of the Lesson

In this lesson, students will be shown how to use a T1-83 graphing calculator to solve linear and quadratic equations. The specific keys students will be introduced to include: [Y=], [GRAPH], [WINDOW], [ZOOM], [TRACE], [2nd][GRAPH], and [2nd][WINDOW]. Students will also be shown strategies on how to use the keys on the graphing calculator to show a complete graph.

## Student Objectives

In this lesson, students will:

- Learn how to graph linear equations on the graphing calculator using the [Y=] and [WINDOW] keys.
- Learn how to graph quadratic equations on the graphing calculator using the [Y=] and [WINDOW] keys.
- Learn how to adjust the viewing window using the [WINDOW] key and typing in new values for Xmin, Xmax, Xsc1, Ymin, Ymax, Ysc1, and Xres.
- Learn to use the trace and table features on the calculator to find multiple solutions to a quadratic equation.
- Learn how to find the complete graphs of quadratic equations.

## Learning Activities

1) The first activity will be showing students how to graph an equation in the graphing calculator. Lead the students through graphing the following equation (shown as the buttons that need to be pressed): [Y=]2X^3+15X^{2}+7X and pressing the [GRAPH] button to see the graph on the viewing window.

2) Next, show students how to adjust the viewing window to get a better "picture" of the graph. Instruct students to press the [WINDOW] button and explain how to adjust the Xmin, Xmax, Xsc1, Ymin, Ymax, Ysc1, and Xres values. In addition, explain what adjusting these values do (adjust the range on the x- and y-axis, changing the scale of the graph in one or both axes).

3) The following activity will show students how to find multiple solutions on a graph by using the [TRACE] and [TABLE] features. With the same equation in the Y= field, instruct students to enter the trace mode by pressing the [TRACE] button and direct their attention to the bottom of the screen where the x and y values corresponding to the cursor on the graph are displayed. Have the students press the left and right arrow buttons to move the cursor and watch the values associated with the cursor change according to its location. Show the students what happens when a specific value for x (such as 6, 10, 20, and so on).

4) To use the Table function (such as cases where one wants to find coordinate values that are very large), have the students press the [TRACE] button and set the value for TblStart to 75. The students will observe the table displays 6 values in each column at a time. Explain to the students that they can move up and down the table by pressing the up and down arrow keys.

5) Conclude the lesson by asking students if they have any questions, and reiterate the concepts covered if necessary.