MAT099 Graphing Calculator Activities

Bunker Hill Community College Mathematics Department

Graphing Calculator Activities MAT 099 Intermediate Algebra

1 Graphing Calculator Activities

Instructor’s Guide

Chapter/Focus Objective Notes Graphing Calculator Scavenger Hunt

• Students will become familiar with various functions on the graphing calculator.

• Students will learn how to graph a linear equation using the graphing calculator.

Ch. 10 Polynomials: Operations 10.3 Introduction to Polynomials

Using the Graph to Evaluate X-‐Values • Using the graphing calculator, students will

learn how to use a graph of a function to find a y-‐value for a given x.

Ch. 11 Polynomials: Factoring 11.7 Solving Quadratic Equations by Factoring

What is the Connection between Solving by Factoring and X-‐intercepts?

• Through discovery, students will make connections between the solution of a quadratic equation by factoring and the x-‐intercepts or zeroes of a graph.

• Students will learn how find x-‐intercepts of a graph using a graphing calculator.

**Students should have learned how to solve quadratic equations by factoring before doing this activity.

Ch. 12 Polynomials: Rational Expressions and Equations 12.9 Direct Variation and Inverse Variation

The Golden Ratio • Students will explore the golden ratio, as a

constant in an equation of direct variation. • Students will learn how to create a linear

regression equation using the graphing calculator.

**Each team will need a tape measure. **The instructor will need to help students make a connection that a direct variation relationship, such as in this case, is a special linear function with y intercept 0.

Ch. 14 Radical Expressions and Equations 14.5 Radical Equations

Solving Radical Equations • Students will solve radical equations by

graphing with the graphing calculator. • Students will discover that they can check

solutions that were solved algebraically, by using the graphing calculator.

**Students should have learned how to solve radical equations algebraically before doing this activity.

Ch. 15 Quadratic Equations

Graphing Quadratic Equations. • Through discovery, students will make a

connection between quadratic equations and parts of a parabola.

• Students will learn how to find the vertex of a parabola using the graphing calculator.

**Students should do this activity before the instructor teaches Section 15.6.


TI-‐83 Plus


Name: ______________________ Graphing Calculator Scavenger Hunt

1. Press 2nd, +, ENTER. What is the ID# of your calculator? ____________________ 2. For help, what website can you visit? _________________________________________ 3. Type the number 1234, then ENTER. You should see the same number in the display. Now type the number 9,876,543,210,987,654, then ENTER. Is the identical number displayed? ________ 4. What happens to the screen when you push 2nd, ▲ , 2nd, ▲ , 2nd, ▲ …. ________________________________________________________________________. Press 2nd and then hold down ▲ . Describe what happens: _______________________. 5. ^ is called the "caret" button, and is used to raise a number to a power. Find 65

= _____ To square a number press the number, x2 and ENTER. What is 562? _______ To cube a number, press the number, MATH, select option 3 and press ENTER. What is 363? ___________ Press 2, MATH and choose option 5, then press 1, 6 and ENTER. What did this option do? __________________________________________________ 6. Equations: y = 2x. Press Y=. Clear any equations that are present. Next we enter the equation by positioning the cursor beside “Y1=” and press 2, X,T,θ ,n. To create a table: Press 2nd, WINDOW (which takes you into the Table Set window). Set the TblStart = -2 and ▲Tbl = 1 (this adds 1 to the preceding x-value). To display the table, we press 2nd, GRAPH (which takes you the Table window).

What is the value of Y1, when X is 6? ________________


To create a graph: Press Y=. Make sure that the Plot1, Plot2, Plot 3 at the top of the screen are not highlighted. If they are, move the cursor to the one that is highlighted and press ENTER. That will un-highlight it. Press ZOOM, 6 to select a standard viewing window and display the graph. Draw the graph:

7. Enter (-2)2

into the calculator, what answer did you get? ___________ Now enter –22

into the calculator, what answer did you get this time? ________ Why do you think you got two different answers? ______________________________


Chapter 10 Polynomials: Operations

Using the Graph to Evaluate Y-‐Values

This activity corresponds to Section 10.3 in the textbook, Calculator Corner p. 758. To evaluate the polynomial –x2 – 3x + 1, when x = -‐4, we must first graph y1= –x2 – 3x + 1 (See previous graphing calculator activity). We will use the standard window. Then press 2nd, TRACE (which is actually the CALC function) and select option 1. This will prompt you to enter the x value that you wish to evaluate. Press (-‐), 4, ENTER. The corresponding y value, -‐3 should come up.

Use this process to evaluate each polynomial for the given values of x. Polynomial Equation y = -‐x2 – 3x + 1

x = -‐2, y = ________

x = -‐0.5, y = ________

x = 4, y = ________

y = 3x2 – 5x + 2

x = -‐3, y = ________

x = 1, y = ________

x = 2.6, y = ________

y = 5 -‐ x2

x = -‐3, y = ________

x = -‐1, y = ________

x = 1.5, y = ________

y = 6x3 – 6x

x = -‐1, y = ________

x = -‐0.5, y = ________

x = 1.1, y = ________


Chapter 11 Polynomials: Factoring

What is the connection between solving by factoring and x-‐intercepts?

This activity corresponds to Section 11.7 in the textbook, Calculator Corner p. 880. In this activity, you will:

1. Solve each quadratic equation using the factoring method 2. Graph each quadratic function using the graphing calculator (previous graphing calculator

activity). In order to graph, you must make sure each equation is written with 0 on one side. For example, in #2, you will need to first subtract 6x and add 9 to both sides of the equation before you can enter the function in the graphing calculator. When graphing, use the standard window.

3. Find the x-‐intercepts for the graph. The x-‐intercepts of the graph are also known as the zeroes. After you graph the function, we use the ZERO feature from the CALC menu to find

the x-‐intercepts. Press 2nd, TRACE (which is actually the CALC function) and select option 2: zero. The prompt “Left Bound?” appears. We use the < or > key to move the cursor

to the left of the intercept and press ENTER. Now the prompt “Right Bound?” appears.

Then we move the cursor to the right of the intercept and press ENTER . The prompt

“Guess?” appears. We move the cursor close to the intercept and press ENTER again. The coordinates of the x-‐intercept or zeros should appear. This is one solution of the equation. We can repeat this procedure to find the other x-‐intercept.

Solve by Factoring Graph the original function What are the x-‐intercepts? 1. x2 -‐ x -‐ 6 = 0


Solve by Factoring Graph the original function What are the x-‐intercepts? 2. x2 = 6x – 9

3. x2 -‐ 4x = 0

4. 9x2 = 16


5. -‐2x2 + 13x -‐ 21 = 0

Do you notice any connection between the solutions when you solve by factoring, the graph, and the x-‐intercepts? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________


Chapter 12 Rational Expressions and Equations

The Golden Ratio

This activity corresponds to Section 12.9 in the textbook. In this activity, you will be divided up into pairs and each of you will help your partner with his/her measurements.

1. Measure and record the following.

2. You will now use this data to construct a line of best fit, using the graphing calculator. Entering the data:

Press STAT and choose option 1: Edit. You will enter your data in this screen. Before that, you must clear any data that is already there. Use the cursor and highlight L1. Press

CLEAR, ENTER. Do the same for L2.

Name List 1 List 2

Your Height, cm Height from floor to naval, cm

Index finger, cm Index finger tip to 2nd knuckle, cm

Length of leg, cm Leg from hip to knee, cm

Length of arm, cm Middle finger to elbow, cm

Height of head, chin to top, cm Chin to top of ear, cm

Top of head to pupil, cm Pupil to bottom of lower lip, cm

Height of head, chin to top, cm Width of head, cm

Tip of nose to chin, cm Top of nose to chin, cm

Tip of nose to chin, cm Pupil to tip of nose, cm

Width of nose, cm Tip of nose to upper lip, cm


Then enter your measurements from List 1 in column L1. Each time you enter a number you

must press ENTER. Next enter your measurements from List 2 in the graphing calculator in column L2.

Graphing the data:

Press 2nd, Y= (which is the STAT PLOT function) and select 1:Plot 1. On the next screen, set up the plot as shown.

To view in the appropriate window, press ZOOM and choose 9:ZoomStat.

Finding a linear regression:

In order to calculate the regression line, you must be in the home screen which you can get

to by pressing 2nd , MODE. Press STAT and use the cursor to highlight CALC. Then you will want to choose option 4:LinReg (ax+b).

Next press 2nd , 1 (which will actually give you L1) Then press in , , 2nd , 2 (which will actually give you L2) and ENTER . This will give you the linear regression equation in the form y = ax + b.


To graph the regression line:

In order to graph the regression line, press Y= ,(making sure you clear any equations that

are already there). Press VARS , select 5:Statistics, use your cursor to highlight EQ, and choose 1:RegEQ. The regression equation you found should have been automatically

entered for the equation Y1. Press GRAPH and the regression will be graphed on the same screen as your scatter plot.

3. Please sketch your scatter plot and regression line. Also, give the equation for your regression line.

Regression Line Equation: _____________________________________

What is the slope & y-‐intercept of this line?


Chapter 14 Radical Expressions and Equations

Solving Radical Equations

This activity corresponds to Section 14.5 in the textbook, Calculator Corner p. 1081. Students will use the graphing calculator to solve or check solutions to radical equations.

Consider the equation 𝑥 − 5 = 𝑥 + 7. First, we will solve it algebraically, using the methods from Section 14.5.

Now we will check our solutions using the graphing calculator. We first graph each side of the equation. Enter y1 = x – 5 and y2 = 𝑥 + 7. Instead of using a standard window, we will adjust the

window so we can see the solution to the graph. Press WINDOW and use the window [-‐2, 12, -‐6, 6].

Xmin = -‐2 Xmax = 12 Xscl = 1 Ymin = -‐6 Ymax = 6 Yscl = 1 Xres = 1

Then press GRAPH to see the graph of the two equations.

In order to find the point of intersection, we will use the INTERSECT feature. Press 2nd , TRACE, (which is the CALC function) and select 5:intersect. The query “First curve?” appears on the screen.

The blinking cursor should already be positioned on the graph of y1. We press ENTER to indicate that this is the first curve involved in the intersection. Next, the query, “Second curve?” appears

and the blinking cursor should be positioned on the graph of y2. We press ENTER to indicate that


this is the second curve. Now it asks, “Guess?”, so use the ← or → keys to move the cursor

close to the point of intersection and press ENTER The coordinates of the point of intersection should appear at the bottom of the screen. Thus the solution of the equation is (9, 4). Note that the graph shows a single solution, whereas the algebraic solution yields two possible solutions, 9 and 2, that must be checked. The check shows that 9 is the only solution.

Solve the following equations first algebraically, then with the graphing calculator:

1. Solve 𝑥 − 1 = 𝑥 + 5

Sketch the graph:


2. Solve 3 + 27 − 3𝑥 = 𝑥

Sketch the graph:


Chapter 15 Quadratic Equations

This activity corresponds to Section 15.6 in the textbook. In this activity, you will investigate various parts of a parabola, such as the vertex and how these parts relate to a quadratic equation in the form, = 𝑎𝑥! + 𝑏𝑥 + 𝑐 .

For each equation, first identify a, b, & c. Then calculate 𝒙 = − 𝒃𝟐𝒂 and substitute back into the

equation to find y.

Then use the graphing calculator to draw a sketch of the graph (we learned how to do this in a previous activity). Next indicate on the table whether the graph opens up or down.

Use the graphing calculator to find the vertex of the graph. To find the vertex, you must first determine if you are looking for a maximum or minimum, depending on whether the graph opens

up or down. Press 2nd , TRACE, (which is the CALC function) and select 3:minimum (if the graph opens up) or select 4:maximum (if the graph opens down). Then the calculator will give a prompt,

“Left Bound?” Use the ← or → keys to move the cursor to the left of the vertex and press

ENTER. The calculator will give a prompt, “Right Bound?” Use the ← or → keys to move the

cursor to the right of the vertex and press ENTER. Now it asks, “Guess?”, so use the ← or → keys to move the cursor close to the point of intersection and press ENTER . The calculator will give you either the minimum or maximum, which is the vertex of the parabola.

Quadratic Equation 𝑦 = 𝑎𝑥! + 𝑏𝑥 + 𝑐

1. What is a, b, and c? 2. Find 𝒙 = − 𝒃

𝟐𝒂

3. Use the x value you found to find the y-‐value, by substituting in the equation.

Graph Opens up or down?

Vertex from the graphing calculator

𝑦 = 𝑥! − 3


Quadratic Equation 𝑦 = 𝑎𝑥! + 𝑏𝑥 + 𝑐

4. What is a, b, and c? 5. Find 𝒙 = − 𝒃

𝟐𝒂

6. Use the x value you found to find the y-‐value, by substituting in the equation.

Graph Opens up or down?

Vertex from the graphing calculator

𝑦 = −3𝑥! + 6𝑥

𝑦 = 𝑥! − 4𝑥 + 4

𝑦 = 5 − 𝑥 − 𝑥!


What observations or connections can you make between the quadratic equation, its graph, vertex

and 𝒙 = − 𝒃𝟐𝒂?

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MAT099 Graphing Calculator Activities

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