# Academic Support Center. Using the TI-83/84+ Graphing Calculator PART II

Size: px
Start display at page:

Transcription

1 Academic Support Center Using the TI-83/84+ Graphing Calculator PART II Designed and Prepared by The Academic Support Center Revised June

2 Using the Graphing Calculator (TI-83+ or TI-84+) Table of Contents Graphing: Entering linear equations using Y= key 3 WINDOW and ZOOM: what do they mean and how do I use them? 3 Using the TRACE key to evaluate 5 Solving quadratic equations using ZERO function 5 Solving quadratic equations using a TABLE 7 Maximum and minimum value of a quadratic equation 8 Solving systems of equations using INTERSECT 10 Plotting points 12 Linear regression 13 Miscellaneous: Trigonometry: converting angles 16 2

3 Entering Linear Equations using Y= key To graph an equation on the TI-83 & TI-84, the equation must be in Y= form. Once the equation is in the proper form, the equation can be graphed easily. EXAMPLE Graph y=3x+4 on your calculator PRESS: Y= and then enter equation. PRESS: ZOOM 6 (Standard) and then you ll have your graph! Plot1 Plot2 Plot3 \Y 1 =3X + 4 \Y 2 = \Y 3 = \Y 4 = \Y 5 = \Y 6 = \Y 7 = Press: GRAPH EXAMPLE Graph 2x+4y= 8 on your calculator Solving for Y produces the equation y= -½ x + 2, so that is what needs to be entered on the Y= screen. This may take some practice, but ultimately using the graphing utility will help you greatly! WINDOW and ZOOM: what do they mean and how do I use them? The WINDOW key, allows you to zoom in and out on your graph. It s similar to a camera lens. For convenience, there are several fixed ZOOM functions, as well as the WINDOW key, which allows you to set your own X and Y parameters. 3

4 Press: WINDOW Your screen should look like this WINDOW Xmin = -10 Xmax = 10 Xscl = 1 Ymin = -10 Ymax = 10 Yscl = 1 Xres = 1 This screen allows you to set maximum and minimum values on your axes. The Xscl and Yscl key sets the way the calculator counts each axis. The window above is set from [-10, 10] on the x-axis, counted off by 1 and the y-axis is set from [-10, 10], counted off by 1, which is known as the standard window. Press the GRAPH key to see the axes. In order to see how the zoom functions manipulate the window, let s enter the equation y=x 2 + 4x - 4 into the calculator in the Y= screen. ZOOM- Standard PRESS: ZOOM 6 This sets your window from -10 to 10 on both the X and Y axis. Many of the graphs you encounter in this course will fit into this window. ZOOM- In Press: ZOOM 2 ENTER If the graph is small and hard to see in the standard window, you may want to try to zoom in. This will shrink the window and make your graph seem bigger. ZOOM- Out Press: ZOOM 3 ENTER If the graph is too large for the window, and you cannot see all that you re looking for, try zooming out. This will make the window larger, and the graph will appear smaller. ***NOTE: You can zoom in and out as many times as necessary to view your graph. 4

5 Using the TRACE key to Evaluate One way to evaluate a graph at a specific point is to use the TRACE key. EXAMPLE Evaluate y=3x-8 for x = 2 PRESS: Y= Enter the equation. PRESS: ZOOM 6 View graph in standard window. PRESS: TRACE Enter the number you wish to evaluate for PRESS: ENTER The bottom of the screen will show the corresponding y value. Your calculator should look like this: Y 1 = 3X-8. X = 2 Y = -2 So, at x = 2, y = -2 is the solution. Solving Quadratic Equations using ZERO function The graphing calculator allows us to solve quadratic equations without factoring! In order to do this you must use the option called ZERO in the 2 nd TRACE Menu. EXAMPLE Solve: y= x 2 + 5x 6 5

6 PRESS: Y= Enter the equation PRESS: ZOOM 6 View the window, is it appropriate? If not, zoom in or out. PRESS: 2 nd CALC (above TRACE) 2(for ZERO) ***This next step can get a little tricky, but with practice it will become more natural. Follow the parabola from left to right (just like you would draw it). Use the and keys to move the cursor through the graph. ***This just moves the cursor either left or right and does not have anything to do with the cursor being above or below the x-axis. For Left Bound - Move the cursor to the left of the x-intercept point. Press ENTER For Right Bound - Move the cursor to the right of the x-intercept point. Press ENTER The calculator will now ask for a Guess - just press ENTER Record the result. In this case it is (-6,0). Now, we must repeat the steps for the 2 nd intercept. For Left Bound - Move the cursor to the left of the x-intercept point. Press ENTER For Right Bound - Move the cursor to the right of the x-intercept point. Press ENTER The calculator will now ask for a Guess - just press ENTER Record the result. In this case it is (1,0). So, the solutions are x= - 6 and 1 6

7 Solving Quadratic Equations using a TABLE Graph your function by using the appropriate window size by zooming in ZOOM 2 ENTER or zooming out ZOOM 3 ENTER Now set up your table by pressing 2 nd followed by WINDOW (*Always choose the same value of X min. Tblstart = value of x-min. Make sure ΔTbl=1) Now press 2 nd followed by GRAPH Under Y 1 scroll down until you get a value of 0 The x value will be your first answer. Repeat these steps as many times as necessary to see all other x-intercepts on your graph. EXAMPLE Solve: y= x 2 + 5x 6 PRESS: Y= Enter the equation PRESS: ZOOM 6 View the window, is it appropriate? If not, zoom in or out. From the graph you will know how many x-intercepts you have. In this example there are 2 x-intercepts, therefore you should have 2 answers. PRESS: WINDOW Copy the value of Xmin Xmin = -10 PRESS: 2 nd WINDOW Set up the table: TblStart = -10 ΔTbl=1 PRESS: 2 nd GRAPH 7

8 View the table. Under Y 1 scroll down until you get a value of 0, copy the X value which is X = -6. Since we have 2 solutions, therefore keep scrolling down under Y 1 until you get to the second 0, copy the X value which is X = 1. So, the solutions are x= - 6 and 1 Maximum and Minimum value of a Quadratic Equation In this section, you will be instructed step-by-step to find the maximum or the minimum point of a quadratic equation. EXAMPLE Determine the maximum or the minimum value of the function: 2 f ( x) x 3x 5 and where it occurs. 1. PRESS: Y= and enter the equation into Y 1 2. PRESS: GRAPH to see a full picture of the graph. Make sure that you see the turning point. If you can not see the turning point, zoom in or out. 3. From the graph, find if there is a minimum value or a maximum value. If the graph is concave up(opens up), then there is a minimum value. If the graph 8

9 is concave down, then there is a maximum value. In this example, there is a minimum value. To find the minimum value: PRESS 2 nd Trace to activate the CALC menu. 4. PRESS: 3 for minimum. If you have a maximum value, you have to PRESS: 4 for maximum. 5. The calculator will say Left Bound? Use the arrow keys to move the cursor to any point left of the minimum point. Press the ENTER key. 6. The calculator will say Right Bound? Move the cursor to any point to the right of the minimum point. Press the ENTER key. 9

10 7. The calculator will say Guess? Press the ENTER key one last time. 8. The coordinates of the minimum point are displayed at the bottom of the screen. In this example, the minimum value of Y is and the minimum value occurs when X is Your final answer is: X = 1.5 Y = -7.5, which means that there is a minimum value of -7.5 at x=1.5. Solving Systems of Equations using INTERSECT Your graphing calculator can be used to solve systems of equations, provided you first solve each equation for y. Their solution can then be calculated using the INTERSECT option in the CALC menu. EXAMPLE Solve the following system of equations: Y=2x+6 2x+y=4 1. In order to solve this system, the second equation must be solved for y. Subtracting 2x from each side produces the equation y = -2x

11 2. PRESS: Y= and enter the first equation in Y 1 and the second in Y 2. Plot1 Plot2 Plot3 \Y 1 =2x + 6 \Y 2 =-2x + 4 \Y 3 = \Y 4 = \Y 5 = \Y 6 = \Y 7 = 3. PRESS: ZOOM 6 and check to make sure you have an appropriate window. 4. To find the solution, PRESS: 2 nd CALC 5 (INTERSECT) 5. The calculator will say first curve? Move the cursor until it is on top of the intersection point. PRESS: ENTER 6. The calculator will say second curve? Move the cursor until it is on top of the intersection point. PRESS: ENTER 7. PRESS: ENTER when the calculator says guess? 8. Record the intersection point. In this case it is (- 1 / 2, 5).. Intersection X=-.5 Y=5 11

12 Plotting Points 1. PRESS STAT 2. PRESS: ENTER or 1 to see the EDIT screen 3. If there is data, clear it by highlighting L1, Press CLEAR and hit ENTER. Repeat this step to clear all the data in the other lists. ***Do not press DEL. 4. ENTER: x-values in L1 and y-values in L2. Make sure to press ENTER after each number. 5. PRESS: Y= 12

13 6. HIGHLIGHT: Plot1 and Press ENTER. Make sure that Plot1 is highlighted. 7. PRESS: ZOOM 9, the window will display all the points that you entered. Linear Regression 1. Enter data into L1 and L2. (See previous section: Plotting points). 13

14 2. PRESS: STAT and highlight CALC by moving the cursor to the right. 3. CHOOSE: 4:LinReg(ax+b) and hit ENTER to find the best fit line equation for the data points that you entered. 4. PRESS: ENTER again to have your line equation. The Line equation is y = x which is in the form y = ax+b 5. To copy the model equation into Y= so that you could graph the equation, GO TO: Y= and clear Y 1. 14

15 6. PRESS: VARS key 7. PRESS: 5:Statistics 8. Move the cursor to the right to highlight EQ. 9. PRESS: ENTER and the model is placed into Y 1. 15

16 10. PRESS: GRAPH to see the graph of your model with the data points. Trigonometry: Converting Angles The calculator can convert angles in Degree, Minutes, and Seconds (D M S ) notation to decimal degree form and vice-versa. Converting from (D M S ) Notation to Decimal Degree Form: EXAMPLE Convert to decimal degree form. 1. PRESS: MODE. Make sure that Degree is highlighted. If not highlighted, move to Degree and press ENTER. 2. Return to the main screen. Enter the number of degrees first, in this case 5. Then PRESS 2 nd APPS (ANGLE) and PRESS 1 for the degrees symbol. 5 16

17 3. Enter the amount of minutes next, 42 in this example. Then PRESS 2 nd APPS (ANGLE) and PRESS 2 for the minutes symbol Enter the amount of seconds next, in this example, 30. Then Press ALPHA and Press + (the addition sign) for the seconds symbol PRESS ENTER Round to the nearest hundredth of a degree. Your Answer is: =

18 Converting Decimal Degree From to (D M S ) Notation: EXAMPLE Convert to D M S notation. 1. PRESS: MODE. Make sure that Degree is highlighted. If not highlighted, move to Degree and press ENTER. 2. To convert decimal degree form to D M S form, we enter into the main screen PRESS 2 nd APPS (ANGLE) and PRESS 4 for DMS. Then PRESS ENTER DMS Your Final Answer is: =

### TI-83/84 Plus Graphing Calculator Worksheet #2

TI-83/8 Plus Graphing Calculator Worksheet #2 The graphing calculator is set in the following, MODE, and Y, settings. Resetting your calculator brings it back to these original settings. MODE Y Note that

### Pre-Calculus Graphing Calculator Handbook

Pre-Calculus Graphing Calculator Handbook I. Graphing Functions A. Button for Functions This button is used to enter any function to be graphed. You can enter up to 10 different functions at a time. Use

### Guide for Texas Instruments TI-83, TI-83 Plus, or TI-84 Plus Graphing Calculator

Guide for Texas Instruments TI-83, TI-83 Plus, or TI-84 Plus Graphing Calculator This Guide is designed to offer step-by-step instruction for using your TI-83, TI-83 Plus, or TI-84 Plus graphing calculator

### Getting to know your TI-83

Calculator Activity Intro Getting to know your TI-83 Press ON to begin using calculator.to stop, press 2 nd ON. To darken the screen, press 2 nd alternately. To lighten the screen, press nd 2 alternately.

### Scatter Plot, Correlation, and Regression on the TI-83/84

Scatter Plot, Correlation, and Regression on the TI-83/84 Summary: When you have a set of (x,y) data points and want to find the best equation to describe them, you are performing a regression. This page

### Introduction to the Graphing Calculator

Unit 0 Introduction to the Graphing Calculator Intermediate Algebra Update 2/06/06 Unit 0 Activity 1: Introduction to Computation on a Graphing Calculator Why: As technology becomes integrated into all

### I. Turn it on: Press É

Graphing Calculator Guide for the TI-83/84 Plus The following pages describe how to use the calculator to graph functions, use some of the matrix menu, use scientific notation, and other various keys.

### Basic Graphing Functions for the TI-83 and TI-84

Basic Graphing Functions for the TI-83 and TI-84 The primary benefits of the TI-83 and TI-84 are the abilities to graph functions and to identify properties those functions possess. The purpose of this

### Introductory Handbook for the TI-89 Titanium

Introductory Handbook for the TI-89 Titanium Note: This handbook will, for the most part, work for the standard TI-89 as well. The color-coding used on the TI-89 differs from the color-coding used on the

### Math Tools Cell Phone Plans

NATIONAL PARTNERSHIP FOR QUALITY AFTERSCHOOL LEARNING www.sedl.org/afterschool/toolkits Math Tools Cell Phone Plans..............................................................................................

### Part V: Texas Instruments TI-92, TI-92 Plus, Voyage 200

Part V: Texas Instruments TI-92, TI-92 Plus, Voyage 200 V.1 Getting started with the TI-92, TI-92 Plus, Voyage 200 Note: All keystroke sequences given for the Voyage 200 are applicable to the TI-92 and

74 In the Herb Business, Part III Factoring and Quadratic Equations In the herbal medicine business, you and your partner sold 120 bottles of your best herbal medicine each week when you sold at your original

### Activity 6 Graphing Linear Equations

Activity 6 Graphing Linear Equations TEACHER NOTES Topic Area: Algebra NCTM Standard: Represent and analyze mathematical situations and structures using algebraic symbols Objective: The student will be

### Calculator Notes for the TI-89, TI-92 Plus, and Voyage 200

CHAPTER 1 Note 1A Reentry Calculator Notes for the TI-89, TI-92 Plus, and Voyage 200 If you want to do further calculation on a result you ve just found, and that result is the first number in the expression

### Equations, Lenses and Fractions

46 Equations, Lenses and Fractions The study of lenses offers a good real world example of a relation with fractions we just can t avoid! Different uses of a simple lens that you may be familiar with are

### EASY STEPS TO SUCCESS: A GRAPHING CALCULATOR GUIDE

EASY STEPS TO SUCCESS: A GRAPHING CALCULATOR GUIDE TO ACCOMPANY MATHEMATICAL APPLICATIONS FOR THE MANAGEMENT, LIFE, AND SOCIAL SCIENCES EIGHTH EDITION HARSHBARGER/REYNOLDS LISA S. YOCCO Georgia Southern

### How Does My TI-84 Do That

How Does My TI-84 Do That A guide to using the TI-84 for statistics Austin Peay State University Clarksville, Tennessee How Does My TI-84 Do That A guide to using the TI-84 for statistics Table of Contents

Problem 1 The Parabola Examine the data in L 1 and L to the right. Let L 1 be the x- value and L be the y-values for a graph. 1. How are the x and y-values related? What pattern do you see? To enter the

### TI-83 GRAPHING CALCULATOR BASIC OPERATIONS by Carolyn Meitler Concordia University Wisconsin

TI-83 GRAPHING CALCULATOR BASIC OPERATIONS by Carolyn Meitler Concordia University Wisconsin B-1 Getting Started Press ON to turn on the calculator. Press 2nd + to get the MEMORY screen (shown at the right).

### Linear Equations. 5- Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber

Linear Equations 5- Day Lesson Plan Unit: Linear Equations Grade Level: Grade 9 Time Span: 50 minute class periods By: Richard Weber Tools: Geometer s Sketchpad Software Overhead projector with TI- 83

### Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c

Unit 7 Quadratic Relations of the Form y = ax 2 + bx + c Lesson Outline BIG PICTURE Students will: manipulate algebraic expressions, as needed to understand quadratic relations; identify characteristics

### EL-9650/9600c/9450/9400 Handbook Vol. 1

Graphing Calculator EL-9650/9600c/9450/9400 Handbook Vol. Algebra EL-9650 EL-9450 Contents. Linear Equations - Slope and Intercept of Linear Equations -2 Parallel and Perpendicular Lines 2. Quadratic Equations

### 1.2 Break-Even Analysis and Market Equilibrium

Math 142 c Roberto Barrera, Fall 2015 1 1.2 Break-Even Analysis and Market Equilibrium Mathematical models of cost, revenue, and profits Two types of costs: 1. Fixed costs: 2. Variable costs: Total cost:

### 2 Describing, Exploring, and

2 Describing, Exploring, and Comparing Data This chapter introduces the graphical plotting and summary statistics capabilities of the TI- 83 Plus. First row keys like \ R (67\$73/276 are used to obtain

### Linear Equations. Find the domain and the range of the following set. {(4,5), (7,8), (-1,3), (3,3), (2,-3)}

Linear Equations Domain and Range Domain refers to the set of possible values of the x-component of a point in the form (x,y). Range refers to the set of possible values of the y-component of a point in

### How To Use The Ti-83+/84+ Calculator For Math 111

Using the TI-83+/84+ Graphing Calculator in Math 111 at Tacoma Community College Version 1.0 Scott MacDonald Copyright c 2005 by Scott MacDonald Permission is given to reproduce this document in whole

### DATA HANDLING AND ANALYSIS ON THE TI-82 AND TI-83/83 PLUS GRAPHING CALCULATORS:

DATA HANDLING AND ANALYSIS ON THE TI-82 AND TI-83/83 PLUS GRAPHING CALCULATORS: A RESOURCE FOR SCIENCE AND MATHEMATICS STUDENTS John L. McClure Scott A. Sinex Barbara A. Gage Prince George s Community

### Graphing Linear Equations

Graphing Linear Equations I. Graphing Linear Equations a. The graphs of first degree (linear) equations will always be straight lines. b. Graphs of lines can have Positive Slope Negative Slope Zero slope

### V. Systems of Equations and Inequalities

VIRGINIA DEPARTMENT OF EDUCATION Worksheets to accompany Videos VIRGINIA STANDARDS OF LEARNING MATHEMATICS AND THE TEXAS INSTRUMENT GRAPHING CALCULATOR Worksheets for SIX PROGRAMS Written by Ellen S. Hook

### Lesson 3 Using the Sine Function to Model Periodic Graphs

Lesson 3 Using the Sine Function to Model Periodic Graphs Objectives After completing this lesson you should 1. Know that the sine function is one of a family of functions which is used to model periodic

### 7.7 Solving Rational Equations

Section 7.7 Solving Rational Equations 7 7.7 Solving Rational Equations When simplifying comple fractions in the previous section, we saw that multiplying both numerator and denominator by the appropriate

### Summary of important mathematical operations and formulas (from first tutorial):

EXCEL Intermediate Tutorial Summary of important mathematical operations and formulas (from first tutorial): Operation Key Addition + Subtraction - Multiplication * Division / Exponential ^ To enter a

### Basic Use of the TI-84 Plus

Basic Use of the TI-84 Plus Topics: Key Board Sections Key Functions Screen Contrast Numerical Calculations Order of Operations Built-In Templates MATH menu Scientific Notation The key VS the (-) Key Navigation

### 6.2 Solving Nonlinear Equations

6.2. SOLVING NONLINEAR EQUATIONS 399 6.2 Solving Nonlinear Equations We begin by introducing a property that will be used extensively in this and future sections. The zero product property. If the product

### Graphing Calculator Workshops

Graphing Calculator Workshops For the TI-83/84 Classic Operating System & For the TI-84 New Operating System (MathPrint) LEARNING CENTER Overview Workshop I Learn the general layout of the calculator Graphing

### (1) S = R, where S is the sum, i is the rate of interest per compounding

Solving Annuity Formulas for Interest Rate Iterative Routines on the TI 83/84 Floyd Vest Basic to mathematics of finance is the formula for the sum of an ordinary annuity. The formula in traditional terminology

### CALCULATOR QUICK REFERENCE GUIDE and INSTRUCTIONS. TI-89 Titanium TI-VOYAGE 200 TI-89

CALCULATOR QUICK REFERENCE GUIDE and INSTRUCTIONS TI-89 Titanium TI-VOYAGE 200 TI-89 BASICS Green diamond: use for items in green above a key 2 nd : use for items in blue above a key(voyage and 89Titanium)

### Calculator Notes for the TI-89, TI-92 Plus, and Voyage 200

CHAPTER 8 Note 8A Changing Mode Calculator Notes for the TI-89, TI-92 Plus, and Voyage 200 For your work in this chapter, check and change, if necessary, three settings. a. Press MODE. In the first line,

### Tutorial for the TI-89 Titanium Calculator

SI Physics Tutorial for the TI-89 Titanium Calculator Using Scientific Notation on a TI-89 Titanium calculator From Home, press the Mode button, then scroll down to Exponential Format. Select Scientific.

### Excel Tutorial. Bio 150B Excel Tutorial 1

Bio 15B Excel Tutorial 1 Excel Tutorial As part of your laboratory write-ups and reports during this semester you will be required to collect and present data in an appropriate format. To organize and

### Definition: A vector is a directed line segment that has and. Each vector has an initial point and a terminal point.

6.1 Vectors in the Plane PreCalculus 6.1 VECTORS IN THE PLANE Learning Targets: 1. Find the component form and the magnitude of a vector.. Perform addition and scalar multiplication of two vectors. 3.

### For another way to generate recursive sequences, see Calculator Note 1D.

!"# If you want to do further calculation on a result you ve just found, and that result is the first number in the expression you now want to evaluate, you can simply continue the expression. For example,

### 7.1 Graphs of Quadratic Functions in Vertex Form

7.1 Graphs of Quadratic Functions in Vertex Form Quadratic Function in Vertex Form A quadratic function in vertex form is a function that can be written in the form f (x) = a(x! h) 2 + k where a is called

### Graphing Linear Equations in Two Variables

Math 123 Section 3.2 - Graphing Linear Equations Using Intercepts - Page 1 Graphing Linear Equations in Two Variables I. Graphing Lines A. The graph of a line is just the set of solution points of the

### Overview. Observations. Activities. Chapter 3: Linear Functions Linear Functions: Slope-Intercept Form

Name Date Linear Functions: Slope-Intercept Form Student Worksheet Overview The Overview introduces the topics covered in Observations and Activities. Scroll through the Overview using " (! to review,

### 10.1. Solving Quadratic Equations. Investigation: Rocket Science CONDENSED

CONDENSED L E S S O N 10.1 Solving Quadratic Equations In this lesson you will look at quadratic functions that model projectile motion use tables and graphs to approimate solutions to quadratic equations

### FACTORING QUADRATICS 8.1.1 and 8.1.2

FACTORING QUADRATICS 8.1.1 and 8.1.2 Chapter 8 introduces students to quadratic equations. These equations can be written in the form of y = ax 2 + bx + c and, when graphed, produce a curve called a parabola.

### MSLC Workshop Series Math 1148 1150 Workshop: Polynomial & Rational Functions

MSLC Workshop Series Math 1148 1150 Workshop: Polynomial & Rational Functions The goal of this workshop is to familiarize you with similarities and differences in both the graphing and expression of polynomial

### Introduction to the TI-Nspire CX

Introduction to the TI-Nspire CX Activity Overview: In this activity, you will become familiar with the layout of the TI-Nspire CX. Step 1: Locate the Touchpad. The Touchpad is used to navigate the cursor

Quadratic Functions Applications CA 8.0 Students solve and graph quadratic equations by using the quadratic formula. Students apply these techniques in solving word problems. Today you will be investigating/experiencing

### Absorbance Spectrophotometry: Analysis of FD&C Red Food Dye #40 Calibration Curve Procedure

Absorbance Spectrophotometry: Analysis of FD&C Red Food Dye #40 Calibration Curve Procedure Note: there is a second document that goes with this one! 2046 - Absorbance Spectrophotometry. Make sure you

### APPLYING PRE-CALCULUS/CALCULUS SHARP EL-9600. Graphing Calculator DAVID P. LAWRENCE

APPLYING PRE-CALCULUS/CALCULUS SHARP U S I N G T H E EL-9600 Graphing Calculator DAVID P. LAWRENCE Applying PRE-CALCULUS/CALCULUS using the SHARP EL-9600 GRAPHING CALCULATOR David P. Lawrence Southwestern

### LAYOUT OF THE KEYBOARD

Dr. Charles Hofmann, LaSalle hofmann@lasalle.edu Dr. Roseanne Hofmann, MCCC rhofman@mc3.edu ------------------------------------------------------------------------------------------------- DISPLAY CONTRAST

### Slope & y-intercept Discovery Activity

TI-83 Graphing Calculator Activity Slope & y-intercept Discovery Activity Justin Vallone 11/2/05 In this activity, you will use your TI-83 graphing calculator to graph equations of lines. Follow the steps

### Casio 9860 Self-Guided Instructions TABLE-GRAPH Mode

Casio 9860 Self-Guided Instructions TABLE-GRAPH Mode Instructions Screenshots Investigating Algebraic Systems in TABLE and GRAPH Modes One of the real advantages of the Graphic Calculator is the speed

### Objectives. Materials

. Objectives Activity 12 To model the process of cooling To use a cooling curve to simulate a forensic scenario to predict the time of death To use technology to find an exponential plot Materials TI-83

### 14 Financial. Functions. Financial Functions 14-1. Contents

14 Financial Functions Contents Getting Started: Financing a Car... 14-2 Getting Started: Computing Compound Interest... 14-3 Using the TVM Solver... 14-4 Using the Financial Functions... 14-5 Calculating

### College Teaching Methods & Styles Journal September 2008 Volume 4, Number 9

Finding Multiple Internal Rates Of Return For A Project With Non-Conventional Cash Flows: Utilizing Popular Financial/Graphing Calculators And Spreadsheet Software Jeng-Hong Chen, Albany State University,

### Chapter Table & Graph

Chapter Table & Graph The Table & Graph menu makes it possible to generate numeric tables from functions stored in memory. You can also use multiple functions to generate tables. Since Table & Graph uses

### Procedure for Graphing Polynomial Functions

Procedure for Graphing Polynomial Functions P(x) = a n x n + a n-1 x n-1 + + a 1 x + a 0 To graph P(x): As an example, we will examine the following polynomial function: P(x) = 2x 3 3x 2 23x + 12 1. Determine

### Elements of a graph. Click on the links below to jump directly to the relevant section

Click on the links below to jump directly to the relevant section Elements of a graph Linear equations and their graphs What is slope? Slope and y-intercept in the equation of a line Comparing lines on

Using Your TI-83/84 Calculator: Linear Correlation and Regression Elementary Statistics Dr. Laura Schultz This handout describes how to use your calculator for various linear correlation and regression

### Using Your TI-89 in Elementary Statistics

Using Your TI-89 in Elementary Statistics Level of Handout: Target: Intermediate users of the TI-89. If you are a new user, pair up with someone in the class that is a bit familiar with the TI-89. You

### Lesson 9.1 Solving Quadratic Equations

Lesson 9.1 Solving Quadratic Equations 1. Sketch the graph of a quadratic equation with a. One -intercept and all nonnegative y-values. b. The verte in the third quadrant and no -intercepts. c. The verte

### Calculator Notes for the CFX-9850GB Plus

CHAPTER 1 Calculator Notes for the Note 1A Entering Lists The calculator contains six folders, each with six preset lists. You can enter 255 elements into a list if enough memory is available. You can

### TI-83 GRAPHING CALCULATOR GUIDEBOOK

TI-83 GRAPHING CALCULATOR GUIDEBOOK TI-GRAPH LINK, Calculator-Based Laboratory, CBL, CBL 2, Calculator-Based Ranger, CBR, Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas Instruments

### 1.3. Maximum or Minimum of a Quadratic Function. Investigate A

< P1-6 photo of a large arched bridge, similar to the one on page 292 or p 360-361of the fish book> Maximum or Minimum of a Quadratic Function 1.3 Some bridge arches are defined by quadratic functions.

### Graphing Parabolas With Microsoft Excel

Graphing Parabolas With Microsoft Excel Mr. Clausen Algebra 2 California State Standard for Algebra 2 #10.0: Students graph quadratic functions and determine the maxima, minima, and zeros of the function.

### SAMPLE. Computer Algebra System (Classpad 330 using OS 3 or above) Application selector. Icolns that access working zones. Icon panel (Master toolbar)

A P P E N D I X B Computer Algebra System (Classpad 330 using OS 3 or above) B.1 Introduction For reference material on basic operations of the calculator, refer to the free downloadable documentation

### Lecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20

Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding

### PARABOLAS AND THEIR FEATURES

STANDARD FORM PARABOLAS AND THEIR FEATURES If a! 0, the equation y = ax 2 + bx + c is the standard form of a quadratic function and its graph is a parabola. If a > 0, the parabola opens upward and the

### M 1310 4.1 Polynomial Functions 1

M 1310 4.1 Polynomial Functions 1 Polynomial Functions and Their Graphs Definition of a Polynomial Function Let n be a nonnegative integer and let a, a,..., a, a, a n n1 2 1 0, be real numbers, with a

### Answer Key Building Polynomial Functions

Answer Key Building Polynomial Functions 1. What is the equation of the linear function shown to the right? 2. How did you find it? y = ( 2/3)x + 2 or an equivalent form. Answers will vary. For example,

### Graphic Designing with Transformed Functions

Name Class The teacher will display the completed example to the right as an example to re-create. Work to make the image of the letter M on your handheld. Transformations of parabolas, domain restrictions,

### Irrational Numbers. A. Rational Numbers 1. Before we discuss irrational numbers, it would probably be a good idea to define rational numbers.

Irrational Numbers A. Rational Numbers 1. Before we discuss irrational numbers, it would probably be a good idea to define rational numbers. Definition: Rational Number A rational number is a number that

### Topic Area: Circles. Definitions. Formulas Distance Formula: D = ( x x ) + ( y ) Equation of a Circle: Activity 8 Algebra II with the Casio fx-9750gii

Where Did That Come From? Teacher Notes Topic Area: Circles NCTM Standards: Use symbolic algebra to represent and explain mathematical relationships. Use geometric models to gain insights into, and answer

### USING A TI-83 OR TI-84 SERIES GRAPHING CALCULATOR IN AN INTRODUCTORY STATISTICS CLASS

USING A TI-83 OR TI-84 SERIES GRAPHING CALCULATOR IN AN INTRODUCTORY STATISTICS CLASS W. SCOTT STREET, IV DEPARTMENT OF STATISTICAL SCIENCES & OPERATIONS RESEARCH VIRGINIA COMMONWEALTH UNIVERSITY Table

### Scientific Graphing in Excel 2010

Scientific Graphing in Excel 2010 When you start Excel, you will see the screen below. Various parts of the display are labelled in red, with arrows, to define the terms used in the remainder of this overview.

### Linear Approximations ACADEMIC RESOURCE CENTER

Linear Approximations ACADEMIC RESOURCE CENTER Table of Contents Linear Function Linear Function or Not Real World Uses for Linear Equations Why Do We Use Linear Equations? Estimation with Linear Approximations

### MODERN APPLICATIONS OF PYTHAGORAS S THEOREM

UNIT SIX MODERN APPLICATIONS OF PYTHAGORAS S THEOREM Coordinate Systems 124 Distance Formula 127 Midpoint Formula 131 SUMMARY 134 Exercises 135 UNIT SIX: 124 COORDINATE GEOMETRY Geometry, as presented

Introduction to Quadratic Functions The St. Louis Gateway Arch was constructed from 1963 to 1965. It cost 13 million dollars to build..1 Up and Down or Down and Up Exploring Quadratic Functions...617.2

### Vocabulary Words and Definitions for Algebra

Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

### Part 1: Background - Graphing

Department of Physics and Geology Graphing Astronomy 1401 Equipment Needed Qty Computer with Data Studio Software 1 1.1 Graphing Part 1: Background - Graphing In science it is very important to find and

### What are the place values to the left of the decimal point and their associated powers of ten?

The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything

### Chapter. Formulas for linear recursion between three terms, made up of an+2, an+1, an, and n

Chapter 16 Recursion Table and Graph You can input two formulas for any of the three following types of recursion, which you can then use to generate a table and draw graphs. General term of sequence {an},

### Activity 5. Two Hot, Two Cold. Introduction. Equipment Required. Collecting the Data

. Activity 5 Two Hot, Two Cold How do we measure temperatures? In almost all countries of the world, the Celsius scale (formerly called the centigrade scale) is used in everyday life and in science and

### Introduction Assignment

PRE-CALCULUS 11 Introduction Assignment Welcome to PREC 11! This assignment will help you review some topics from a previous math course and introduce you to some of the topics that you ll be studying

### www.mathsbox.org.uk ab = c a If the coefficients a,b and c are real then either α and β are real or α and β are complex conjugates

Further Pure Summary Notes. Roots of Quadratic Equations For a quadratic equation ax + bx + c = 0 with roots α and β Sum of the roots Product of roots a + b = b a ab = c a If the coefficients a,b and c

### 3.2. Solving quadratic equations. Introduction. Prerequisites. Learning Outcomes. Learning Style

Solving quadratic equations 3.2 Introduction A quadratic equation is one which can be written in the form ax 2 + bx + c = 0 where a, b and c are numbers and x is the unknown whose value(s) we wish to find.

### Updates to Graphing with Excel

Updates to Graphing with Excel NCC has recently upgraded to a new version of the Microsoft Office suite of programs. As such, many of the directions in the Biology Student Handbook for how to graph with

### Prentice Hall Mathematics, Algebra 1 2009

Prentice Hall Mathematics, Algebra 1 2009 Grades 9-12 C O R R E L A T E D T O Grades 9-12 Prentice Hall Mathematics, Algebra 1 Program Organization Prentice Hall Mathematics supports student comprehension

### Higher Education Math Placement

Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

### EXCEL Tutorial: How to use EXCEL for Graphs and Calculations.

EXCEL Tutorial: How to use EXCEL for Graphs and Calculations. Excel is powerful tool and can make your life easier if you are proficient in using it. You will need to use Excel to complete most of your

### 6.1 Add & Subtract Polynomial Expression & Functions

6.1 Add & Subtract Polynomial Expression & Functions Objectives 1. Know the meaning of the words term, monomial, binomial, trinomial, polynomial, degree, coefficient, like terms, polynomial funciton, quardrtic

### If we denote the monthly payment by p, then we can compute the balance after one month as

Introduction to Modeling 6.2-1 6.2 How to Manage Credit Suppose you have a credit card with the Students R Us bank. When you started college, they gave you a credit card without requiring any credit history.

### is the degree of the polynomial and is the leading coefficient.

Property: T. Hrubik-Vulanovic e-mail: thrubik@kent.edu Content (in order sections were covered from the book): Chapter 6 Higher-Degree Polynomial Functions... 1 Section 6.1 Higher-Degree Polynomial Functions...

### (Least Squares Investigation)

(Least Squares Investigation) o Open a new sketch. Select Preferences under the Edit menu. Select the Text Tab at the top. Uncheck both boxes under the title Show Labels Automatically o Create two points