By: Christopher Imm Johnson County Community College October 7, 2017

Slides:

Advertisements

Similar presentations

Chapter 2 Functions and Graphs.

Advertisements

7-5 Roots and Zeros 7-6 Rational Zero Theorem

Notes 6.6 Fundamental Theorem of Algebra

$100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300 $400 $500 $100 $200 $300.

Limit and Continuity.

Mathematics Topics Table of Contents. 9/14/2013 Tables of Contents 2 How to Use Topics Main Topics Numbers Real Numbers Numbers and Data Numbers & Geometry.

Precalculus CST Released Items Aligned to Stewart Text

THE REAL NUMBERS College Algebra. Sets Set notation Union of sets Intersection of sets Subsets Combinations of three or more sets Applications.

Section 5.5 – The Real Zeros of a Rational Function

7.4 Solving Polynomial Equations Objectives: Solve polynomial equations. Find the real zeros of polynomial functions and state the multiplicity of each.

Lesson 2.5 The Fundamental Theorem of Algebra. For f(x) where n > 0, there is at least one zero in the complex number system Complex → real and imaginary.

Preview of Calculus.

Calculus and Analytic Geometry II

Sullivan Algebra and Trigonometry: Section 5.6 Complex Zeros; Fundamental Theorem of Algebra Objectives Utilize the Conjugate Pairs Theorem to Find the.

Ch 1 – Functions and Their Graphs Different Equations for Lines Domain/Range and how to find them Increasing/Decreasing/Constant Function/Not a Function.

Overview of MAC1105 College Algebra. 1. Graph Circles 2. Find Equations of Circles.

SWBAT: −Match functions to their parent graphs −Find domain and range of functions from a graph −Determine if a function is even or odd −Give the domain.

The Rational Root Theorem.  Is a useful way to find your initial guess when you are trying to find the zeroes (roots) of the polynomial.  THIS IS JUST.

6.6 The Fundamental Theorem of Algebra

POLYNOMIAL, RATIONAL, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS College Algebra.

Polynomials Integrated Math 4 Mrs. Tyrpak. Definition.

Section 2.1 Complex Numbers. The Imaginary Unit i.

Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Chapter 2 Polynomial, Power, and Rational Functions.

Warm Up. Find all zeros. Graph.. TouchesThrough More on Rational Root Theorem.

Chapter 2 Polynomial and Rational Functions. Warm Up

WARM-UP: 10/30/13 Find the standard form of the quadratic function. Identify the vertex and graph.

1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 3 Polynomial and Rational Functions.

MATH 1314 JEOPARDY $7500 $7400$7300$7200$7100$7000$6900$6800$6700$6600$6500$6400$6300$6200$6100$6000$5900$5800$5700$5600$5500$5400$5300$5200$5100$5000$4900$4800$4700$4600$4500$4400$4300$4200$4100$4000$3900$3800$3700$3600$3500$3400$3300$3200$3100$3000$2900

Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley Slide 2- 1.

Specialist Mathematics Polynomials Week 3. Graphs of Cubic Polynomials.

Slide Copyright © 2009 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc.

Warm-up Multiply the factors and write in standard form.

Holt McDougal Algebra 2 Rational Functions Holt Algebra 2Holt McDougal Algebra 2 How do we graph rational functions? How do we transform rational functions.

Solve polynomial equations with complex solutions by using the Fundamental Theorem of Algebra. 5-6 THE FUNDAMENTAL THEOREM OF ALGEBRA.

Algebra Finding Real Roots of Polynomial Equations.

Accelerated Learning-Moving Ahead CCBC Developmental Math to College Algebra Kate Abromaitis and Kathy Baranoski Community College of Baltimore County.

Algebra 2. Solve for x Algebra 2 (KEEP IN MIND THAT A COMPLEX NUMBER CAN BE REAL IF THE IMAGINARY PART OF THE COMPLEX ROOT IS ZERO!) Lesson 6-6 The Fundamental.

1.2 Mathematical Models: A Catalog of Essential Functions

Calculus, Section 1.3.

HOMEWORK CHECK.

2016 Fall OpenStax class ABAC : EUNKYUNG YOU.

3.4 Zeros of Polynomial Functions

Section 6.6 The Fundamental Theorem of Algebra

Review Chapter 2 Sections

Warm-up Multiply the factors and write in standard form.

2.5 Zeros of Polynomial Functions

Finding Real Roots of Polynomial Equations

5-5 Theorems About Roots of Polynomial Equations

3.8 Complex Zeros; Fundamental Theorem of Algebra

Mid term Skills review.

Linear and Quadratic Functions and Modeling

Copyright © Cengage Learning. All rights reserved.

Lesson 2.5 The Fundamental Theorem of Algebra

4.2 Properties of Polynomial Graphs

College Algebra Chapter 3 Polynomial and Rational Functions

Functions, Graphs, and Limits

Test 1: Limit of a Function

Algebra 2 Honors Back To School

Remainder/ Factor Theorem End Behavior Zeros / Graphs Polynomials

3.4 Zeros of Polynomial Functions: Real, Rational, and Complex

Rational Functions .

Rational Root Theorem.

The Factor Theorem A polynomial f(x) has a factor (x − k) if and only if f(k) = 0.

MATHEMATICS (ELECTIVE)

Analysis Portfolio By: Your Name.

4.3: Polynomial Functions

Apply the Fundamental Theorem of Algebra

1) Find f(g(x)) and g(f(x) to show that f(x) and g(x) are inverses

1.2 Essential Functions.

Presentation transcript:

By: Christopher Imm Johnson County Community College October 7, 2017 27th Annual Mathematics Technology Expo Using (Free) Web Tools to Engage the Flipped Classroom and online learning By: Christopher Imm Johnson County Community College October 7, 2017

The Flipped Classroom: At JCCC there is a movement toward the Learning Studio which promotes: Group Learning Inter(active) Learning More student to student interaction More student/teacher interaction Individual and mobile computers for student and group exploration

Activities which drive the topic: Use the Transformation of Functions Exploration to fill in the class notes

Activities to explore topics: Match My Parabola Exploration

Inverse Function Exploration After using this exploration, list a few generalizations about inverse functions. If a point (x,y) is on a function, (y,x) is on the inverse. Inverse functions are symmetric about the line y=x. Sometimes the domain must be restricted for inverse functions to exist.

Explorations and projects used to help define mathematical topics and definitions: The Magic Carpet Ride Sequence Linear Combination Exploration for visualization Magic Carpet Ride Project (informal/concrete idealization) Follow up Project (formalizes mathematical topics definitions)

Explorations which help visualize skills (Wolfram Demonstrations Projects) Matrix Multiplication Planes and Gaussian Elimination of a 3x3 Linear System 3x3 Determinants with Cofactor Expansion Coordinates Relative to a Basis in 2D The Gram Schmidt Process in 3D

Online Class Challenges Providing students with tools to conceptualize the topics Providing students with tools to interact with the topics Providing students with tools to practice with the topics Providing students with tools that offer instantaneous feedback

Applied Calculus Explorations College Algebra Explorations Secant to Tangent Line Exploration Continuity at a Point Exploration Continuity at a Point Follow up Questions Function or not Even function exploration Odd function exploration Composition of functions exploration Factors and zeros of polynomials Quartic function Exploration Rational function exploration Exponential function exploration Logarithmic function exploration

“Drillmaster Assignments” Graph the Line Through Two Points Point Slope Form of a Linear Equation Composition of Functions Computing Inverse Functions Synthetic Division Rational Function Attributes Solving Logarithmic Equations

Quartic Function Exploration What can you conjecture about polynomials from this exploration regarding: End behavior Zeros

Quartic Function Exploration (Cont.) What theorems can you visualize? The Conjugate Zeros Theorem Polynomials of odd degree have at least one real zero The Intermediate Value Theorem