Polynomial Functions

• • Explanation

    • Notes | Annotated

  • Practice Problems

    • Worksheet #1

    • Desmos Activity: Translation of Cubic Functions (teacher use)

• • Explanation:

    • Notes | Annotated

    • Khan article: End behavior of polynomials

    • Khan video: Intro to end behavior of polynomials (8:09)

    • Khan video: End behavior of functions & their graphs (all content) (2:22)

  • Practice Problems

    • Khan Exercise: End behavior of polynomials (all in standard form)

    • Worksheet #1 

• • Explanation

    • Notes | Annotated

    • Khan video: Zeros of polynomials introduction (5:08)

    • Khan video: Zeros of polynomials: plotting zeros (3:18)

    • Khan video: Zeros of polynomials: matching equation to zeros (3:50)

    • Khan video: Zeros of polynomials: matching equation to graph (3:00)

    • Khan video: Zeros of polynomials (with factoring): grouping (4:54)

    • Khan video: Zeros of polynomials (with factoring): common factor (3:31)

    • Khan video: Factoring higher-degree polynomials (8:01)

  • Practice Problems

    • Khan Exercise: Zeros of polynomials (factored form)

    • Khan Exercise: Zeros of polynomials (with factoring)

    • IXL: Algebra 2 L.8 Find the roots of factored polynomials

    • IXL: Algebra 2 L.9 Write a polynomial from its roots 

    • IXL: Algebra 2: L.16 Fundamental Theorem of Algebra (honors)

    • Worksheet #1

Explanation:

• Fundamental Theorem of Algebra

  • Complex conjugates

  • Rational Root Theorem: list the possible rational roots (a type of real roots)

  • Descartes' Rules of Signs: number of real positive and real negative roots

Practice Problems:

• IXL: Algebra 2: L.10 Rational root theorem

• IXL: Algebra 2: L.13 Descartes' Rule of Signs

• • Explanation:

    • Notes | Annotated

    • Khan video: Increasing, decreasing, positive or negative intervals  (Algebra 1) (5:55) - general understanding

    • Khan video: Worked example: positive & negative intervals (Algebra 1)  (1:10) - general understanding

    • Khan video: Positive and negative intervals of polynomials  (8:39)

    • Khan article: Positive & negative intervals of polynomials

    • Khan video: Multiplicity of zeros of polynomials (6:35)

    • Khan video: Zeros of polynomials (multiplicity) (4:59)

    • Khan article: Zeros of polynomials & their graphs

    • Khan article: Positive & negative intervals of polynomials

    • Khan article: Graphs of polynomials 

    • Khan article: Graphs of polynomials: Challenge problems

  • Practice problems:

    • Desmos Activity: Positive and Negative Intervals of a Function (teach use only)

    • Khan exercise: Positive and negative intervals (optional)

    • Khan Exercise: Positive & negative intervals of polynomials

    • Khan Exercise: Zeros of polynomials (multiplicity)

    • IXL: Algebra 2 L.14 Match polynomials and graphs (consider the end behavior, zeros, and y-intercepts)

    • Worksheet #1

• • Explanation:

    • Notes | Annotated

    • Khan video: Increasing, decreasing, positive or negative intervals (Algebra 1) (5:55; start the video at 2:34)

    • Khan video: Introduction to minimum and maximum points (Algebra 1) (5:29) uses more math symbols that are not necessary

    • Khan video: Worked example: absolute and relative extrema (Algebra 1) (4:57)

    • Khan video: Polynomial multiplication word problem (Algebra 1 - 2018) (4:18)

    • Khan video: Polynomial word problem: rectangle and circle area (Algebra 1 - 2018) (4:36)

    • Khan video: Polynomial word problem: total value of bills (Algebra 1 - 2018) (1:23)

    • Khan video: Polynomial word problem: area of a window (Algebra 1 - 2018) (4:47)

    • Khan video: Graph interpretation word problem: temperature

    • Khan video: Graph interpretation word problem: basketball

  • Practice Problems:

    • Desmos Activity: Increasing/Decreasing Functions (teacher use only)

    • Khan exercise: Increasing and decreasing intervals (optional)

    • Khan exercise: Relative maxima and minima (Algebra 1)

    • Khan exercise: Absolute maxima and minima (Algebra 1)

    • Khan exercise: Graph interpretation word problems

    • Desmos Activity: Build a Bigger Field (teacher use only)

    • Worksheet #1

• Explanation

  • Notes | Annotated

  • Khan video: Introduction to average rate of change (Algebra 1) (5:30)

  • Khan video: Worked example: average rate of change from graph (Algebra 1) (2:14)

  • Khan video: Worked example: average rate of change from table (Algebra 1) (2:19)

  • Khan video: Average rate of change word problem: table (Algebra 1) (3:39)

  • Khan video: Average rate of change word problem: graph (Algebra 1)  (6:57)

  • Khan article: Average rate of change review (Algebra 1)

  • Khan video: Average rate of change word problem: equation (Algebra 1 - 2018) (4:32)

  • Khan video: Finding average rate of change of polynomials (given an equation)  (4:01)

• Practice Problems

  • IXL: Algebra 1 Q.17 Rate of change: graphs

  • Khan Exercise: Average rate of change word problems (Algebra 1)

  • Khan exercise: Average rate of change: graphs & tables (Algebra 1)

  • Khan Exercise: Average rate of change of polynomials

  • IXL: Algebra 1 Q.16 Rate of change: tables

  • IXL: Algebra 2 D.10 Average rate of change

  • Worksheet #1

• • Explanation:

    • Notes| Annotated

    • Khan video: Function symmetry introduction (5:21)

    • Khan article: Function symmetry introduction (Graphical)

    • Khan video: Even and odd functions: Graphs (3:52)

    • Khan video: Even and odd functions: Tables (Graphical) (4:08)

    • Khan video: Even & odd polynomials (equations)  (Algebra 2 - 2018) (7:22)

    • Khan article: Symmetry of polynomials  (Algebra 2 - 2018)

    • Khan article: Symmetry of algebraic models

    • Desmos example of an odd function

  • Practice Problems

    • Khan Exercise: Even and odd functions: Graphs and tables

    • Khan Exercise: Even & odd functions: Equations  (Algebra 2 - 2018)

    • Worksheet #1

• Explanation

  • Notes | Annotated

  • Math is Fun: Long Division (the website include text and animated explanations)

• • Khan video: Intro to long division of polynomials (12:08)

  • Khan video: Dividing polynomials by linear expressions (3:23)

  • Khan video: Dividing polynomials by linear expressions: missing term (4:31)

  • Khan video: Dividing polynomials with remainders (Algebra - all content: honors: dividing by a quadratic) (6:22)

  • Khan video: Intro to polynomial synthetic division (Algebra - all content) (5:20)

  • Khan video: Dividing polynomials: synthetic division (Algebra - all content) (4:59)

• Practice Problems

• • • Khan exercise: Divide quadratics by linear expressions (with remainders)

    • Khan exercise: Divide polynomials by linear expressions 

  • Worksheet #1

• Teacher Resource

  • • ExamView Test Bank (purchase)

• Explanation

  • Notes | Annotated

  • Khan video: Intro to factors & divisibility  (Algebra 1) (5:25)

  • Khan article: Intro to factors & divisibility (Algebra 1) 

  • Khan video: Factoring using polynomial division (completely factor) (5:57)

  • Khan video: Factoring using polynomial division: missing term (completely factor) (3:57)

  • Khan video: Intro to the Polynomial Remainder Theorem (6:42)

  • Khan video: Remainder theorem: finding remainder from equation (3:31)

  • Khan video: Remainder theorem examples (5:31)

  • Khan video: Using the Polynomial Remainder Theorem: checking factors (3:25)

• Practice Problems

  • Khan Exercise: Factor using polynomial division (Rewrite a function as a product of linear factors)

  • Khan exercise: Remainder theorem

  • Khan Exercise: Remainder theorem and factors

  • Worksheet #1

• Explanation:

  • Summary Notes

• Practice Problems:

  • Concept Connections WS#1

  • Review WS #1

  • Review WS#2

  • Desmos Class activity: Polygraph Polynomial

  • Desmos Activity: Match My Polynomial

  • Desmos Activity: Properties of a graph (sign/direction/concavity) (teacher use only) - ignore concavity slides

  • Cumulative Review WS #2