Academic Support Center. Using the TI83/84+ Graphing Calculator PART II


 Osborn Rose
 5 years ago
 Views:
Transcription
1 Academic Support Center Using the TI83/84+ Graphing Calculator PART II Designed and Prepared by The Academic Support Center Revised June
2 Using the Graphing Calculator (TI83+ or TI84+) 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 TI83 & TI84, 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 xaxis, counted off by 1 and the yaxis 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=3x8 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 = 3X8. 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 xaxis. For Left Bound  Move the cursor to the left of the xintercept point. Press ENTER For Right Bound  Move the cursor to the right of the xintercept 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 xintercept point. Press ENTER For Right Bound  Move the cursor to the right of the xintercept 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 xmin. 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 xintercepts 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 xintercepts you have. In this example there are 2 xintercepts, 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 stepbystep 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: xvalues in L1 and yvalues 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 viceversa. 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: =
TI83/84 Plus Graphing Calculator Worksheet #2
TI83/8 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
More informationPreCalculus Graphing Calculator Handbook
PreCalculus 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
More informationGuide for Texas Instruments TI83, TI83 Plus, or TI84 Plus Graphing Calculator
Guide for Texas Instruments TI83, TI83 Plus, or TI84 Plus Graphing Calculator This Guide is designed to offer stepbystep instruction for using your TI83, TI83 Plus, or TI84 Plus graphing calculator
More informationGetting to know your TI83
Calculator Activity Intro Getting to know your TI83 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.
More informationScatter Plot, Correlation, and Regression on the TI83/84
Scatter Plot, Correlation, and Regression on the TI83/84 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
More informationIntroduction 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
More informationI. Turn it on: Press É
Graphing Calculator Guide for the TI83/84 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.
More informationBasic Graphing Functions for the TI83 and TI84
Basic Graphing Functions for the TI83 and TI84 The primary benefits of the TI83 and TI84 are the abilities to graph functions and to identify properties those functions possess. The purpose of this
More informationIntroductory Handbook for the TI89 Titanium
Introductory Handbook for the TI89 Titanium Note: This handbook will, for the most part, work for the standard TI89 as well. The colorcoding used on the TI89 differs from the colorcoding used on the
More informationMath Tools Cell Phone Plans
NATIONAL PARTNERSHIP FOR QUALITY AFTERSCHOOL LEARNING www.sedl.org/afterschool/toolkits Math Tools Cell Phone Plans..............................................................................................
More informationPart V: Texas Instruments TI92, TI92 Plus, Voyage 200
Part V: Texas Instruments TI92, TI92 Plus, Voyage 200 V.1 Getting started with the TI92, TI92 Plus, Voyage 200 Note: All keystroke sequences given for the Voyage 200 are applicable to the TI92 and
More informationIn the Herb Business, Part III Factoring and Quadratic Equations
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
More informationActivity 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
More informationCalculator Notes for the TI89, TI92 Plus, and Voyage 200
CHAPTER 1 Note 1A Reentry Calculator Notes for the TI89, TI92 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
More informationEquations, 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
More informationEASY 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
More informationHow Does My TI84 Do That
How Does My TI84 Do That A guide to using the TI84 for statistics Austin Peay State University Clarksville, Tennessee How Does My TI84 Do That A guide to using the TI84 for statistics Table of Contents
More informationGraphing Quadratic Functions
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 yvalues for a graph. 1. How are the x and yvalues related? What pattern do you see? To enter the
More informationTI83 GRAPHING CALCULATOR BASIC OPERATIONS by Carolyn Meitler Concordia University Wisconsin
TI83 GRAPHING CALCULATOR BASIC OPERATIONS by Carolyn Meitler Concordia University Wisconsin B1 Getting Started Press ON to turn on the calculator. Press 2nd + to get the MEMORY screen (shown at the right).
More informationLinear 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
More informationUnit 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
More informationEL9650/9600c/9450/9400 Handbook Vol. 1
Graphing Calculator EL9650/9600c/9450/9400 Handbook Vol. Algebra EL9650 EL9450 Contents. Linear Equations  Slope and Intercept of Linear Equations 2 Parallel and Perpendicular Lines 2. Quadratic Equations
More information1.2 BreakEven Analysis and Market Equilibrium
Math 142 c Roberto Barrera, Fall 2015 1 1.2 BreakEven Analysis and Market Equilibrium Mathematical models of cost, revenue, and profits Two types of costs: 1. Fixed costs: 2. Variable costs: Total cost:
More information2 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
More informationLinear 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 xcomponent of a point in the form (x,y). Range refers to the set of possible values of the ycomponent of a point in
More informationHow To Use The Ti83+/84+ Calculator For Math 111
Using the TI83+/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
More informationDATA HANDLING AND ANALYSIS ON THE TI82 AND TI83/83 PLUS GRAPHING CALCULATORS:
DATA HANDLING AND ANALYSIS ON THE TI82 AND TI83/83 PLUS GRAPHING CALCULATORS: A RESOURCE FOR SCIENCE AND MATHEMATICS STUDENTS John L. McClure Scott A. Sinex Barbara A. Gage Prince George s Community
More informationGraphing 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
More informationV. 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
More informationLesson 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
More information7.7 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
More informationSummary 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
More informationBasic Use of the TI84 Plus
Basic Use of the TI84 Plus Topics: Key Board Sections Key Functions Screen Contrast Numerical Calculations Order of Operations BuiltIn Templates MATH menu Scientific Notation The key VS the () Key Navigation
More information6.2 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
More informationGraphing Calculator Workshops
Graphing Calculator Workshops For the TI83/84 Classic Operating System & For the TI84 New Operating System (MathPrint) LEARNING CENTER Overview Workshop I Learn the general layout of the calculator Graphing
More information(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
More informationCALCULATOR QUICK REFERENCE GUIDE and INSTRUCTIONS. TI89 Titanium TIVOYAGE 200 TI89
CALCULATOR QUICK REFERENCE GUIDE and INSTRUCTIONS TI89 Titanium TIVOYAGE 200 TI89 BASICS Green diamond: use for items in green above a key 2 nd : use for items in blue above a key(voyage and 89Titanium)
More informationCalculator Notes for the TI89, TI92 Plus, and Voyage 200
CHAPTER 8 Note 8A Changing Mode Calculator Notes for the TI89, TI92 Plus, and Voyage 200 For your work in this chapter, check and change, if necessary, three settings. a. Press MODE. In the first line,
More informationTutorial for the TI89 Titanium Calculator
SI Physics Tutorial for the TI89 Titanium Calculator Using Scientific Notation on a TI89 Titanium calculator From Home, press the Mode button, then scroll down to Exponential Format. Select Scientific.
More informationExcel Tutorial. Bio 150B Excel Tutorial 1
Bio 15B Excel Tutorial 1 Excel Tutorial As part of your laboratory writeups and reports during this semester you will be required to collect and present data in an appropriate format. To organize and
More informationDefinition: 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.
More informationFor 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,
More information7.1 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
More informationGraphing 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
More informationOverview. Observations. Activities. Chapter 3: Linear Functions Linear Functions: SlopeIntercept Form
Name Date Linear Functions: SlopeIntercept Form Student Worksheet Overview The Overview introduces the topics covered in Observations and Activities. Scroll through the Overview using " (! to review,
More information10.1. 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
More informationFACTORING 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.
More informationMSLC 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
More informationIntroduction to the TINspire CX
Introduction to the TINspire CX Activity Overview: In this activity, you will become familiar with the layout of the TINspire CX. Step 1: Locate the Touchpad. The Touchpad is used to navigate the cursor
More informationQuadratic Functions Applications
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
More informationAbsorbance 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
More informationAPPLYING PRECALCULUS/CALCULUS SHARP EL9600. Graphing Calculator DAVID P. LAWRENCE
APPLYING PRECALCULUS/CALCULUS SHARP U S I N G T H E EL9600 Graphing Calculator DAVID P. LAWRENCE Applying PRECALCULUS/CALCULUS using the SHARP EL9600 GRAPHING CALCULATOR David P. Lawrence Southwestern
More informationLAYOUT OF THE KEYBOARD
Dr. Charles Hofmann, LaSalle hofmann@lasalle.edu Dr. Roseanne Hofmann, MCCC rhofman@mc3.edu  DISPLAY CONTRAST
More informationSlope & yintercept Discovery Activity
TI83 Graphing Calculator Activity Slope & yintercept Discovery Activity Justin Vallone 11/2/05 In this activity, you will use your TI83 graphing calculator to graph equations of lines. Follow the steps
More informationCasio 9860 SelfGuided Instructions TABLEGRAPH Mode
Casio 9860 SelfGuided Instructions TABLEGRAPH Mode Instructions Screenshots Investigating Algebraic Systems in TABLE and GRAPH Modes One of the real advantages of the Graphic Calculator is the speed
More informationStatistics with the TI86
Statistics with the TI86 The TI86 Manual, besides coming with your calculator, can be downloaded or read in a browser in Adobe Acrobat Reader form from http://education.ti.com/product/pdf/gb/ti86book.pdf.
More informationObjectives. 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 TI83
More information14 Financial. Functions. Financial Functions 141. Contents
14 Financial Functions Contents Getting Started: Financing a Car... 142 Getting Started: Computing Compound Interest... 143 Using the TVM Solver... 144 Using the Financial Functions... 145 Calculating
More informationCollege Teaching Methods & Styles Journal September 2008 Volume 4, Number 9
Finding Multiple Internal Rates Of Return For A Project With NonConventional Cash Flows: Utilizing Popular Financial/Graphing Calculators And Spreadsheet Software JengHong Chen, Albany State University,
More informationChapter 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
More informationProcedure for Graphing Polynomial Functions
Procedure for Graphing Polynomial Functions P(x) = a n x n + a n1 x n1 + + 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
More informationElements 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 yintercept in the equation of a line Comparing lines on
More informationCopyright 2007 by Laura Schultz. All rights reserved. Page 1 of 5
Using Your TI83/84 Calculator: Linear Correlation and Regression Elementary Statistics Dr. Laura Schultz This handout describes how to use your calculator for various linear correlation and regression
More informationUsing Your TI89 in Elementary Statistics
Using Your TI89 in Elementary Statistics Level of Handout: Target: Intermediate users of the TI89. If you are a new user, pair up with someone in the class that is a bit familiar with the TI89. You
More informationLesson 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 yvalues. b. The verte in the third quadrant and no intercepts. c. The verte
More informationCalculator Notes for the CFX9850GB 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
More informationTI83 GRAPHING CALCULATOR GUIDEBOOK
TI83 GRAPHING CALCULATOR GUIDEBOOK TIGRAPH LINK, CalculatorBased Laboratory, CBL, CBL 2, CalculatorBased Ranger, CBR, Constant Memory, Automatic Power Down, APD, and EOS are trademarks of Texas Instruments
More information1.3. Maximum or Minimum of a Quadratic Function. Investigate A
< P16 photo of a large arched bridge, similar to the one on page 292 or p 360361of the fish book> Maximum or Minimum of a Quadratic Function 1.3 Some bridge arches are defined by quadratic functions.
More informationGraphing 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.
More informationSAMPLE. 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
More informationLecture 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
More informationPARABOLAS 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
More informationM 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
More informationAnswer 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,
More informationGraphic Designing with Transformed Functions
Name Class The teacher will display the completed example to the right as an example to recreate. Work to make the image of the letter M on your handheld. Transformations of parabolas, domain restrictions,
More informationIrrational 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
More informationTopic Area: Circles. Definitions. Formulas Distance Formula: D = ( x x ) + ( y ) Equation of a Circle: Activity 8 Algebra II with the Casio fx9750gii
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
More informationUSING A TI83 OR TI84 SERIES GRAPHING CALCULATOR IN AN INTRODUCTORY STATISTICS CLASS
USING A TI83 OR TI84 SERIES GRAPHING CALCULATOR IN AN INTRODUCTORY STATISTICS CLASS W. SCOTT STREET, IV DEPARTMENT OF STATISTICAL SCIENCES & OPERATIONS RESEARCH VIRGINIA COMMONWEALTH UNIVERSITY Table
More informationScientific 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.
More informationLinear 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
More informationMODERN 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
More informationIntroduction to Quadratic Functions
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
More informationVocabulary 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
More informationPart 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
More informationWhat 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
More informationChapter. 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},
More informationActivity 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
More informationIntroduction Assignment
PRECALCULUS 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
More informationwww.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
More information3.2. 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.
More informationUpdates 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
More informationPrentice Hall Mathematics, Algebra 1 2009
Prentice Hall Mathematics, Algebra 1 2009 Grades 912 C O R R E L A T E D T O Grades 912 Prentice Hall Mathematics, Algebra 1 Program Organization Prentice Hall Mathematics supports student comprehension
More informationHigher 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
More informationEXCEL 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
More information6.1 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
More informationIf we denote the monthly payment by p, then we can compute the balance after one month as
Introduction to Modeling 6.21 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.
More informationis the degree of the polynomial and is the leading coefficient.
Property: T. HrubikVulanovic email: thrubik@kent.edu Content (in order sections were covered from the book): Chapter 6 HigherDegree Polynomial Functions... 1 Section 6.1 HigherDegree Polynomial Functions...
More information(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
More informationProbability Distributions
CHAPTER 6 Probability Distributions Calculator Note 6A: Computing Expected Value, Variance, and Standard Deviation from a Probability Distribution Table Using Lists to Compute Expected Value, Variance,
More informationprice quantity q The Supply Function price quantity q
Shown below is another demand function for price of a pizza p as a function of the quantity of pizzas sold per week. This function models the behavior of consumers with respect to price and quantity. 3
More information