HSF-IF.C.7c

Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

 
41 Lesson(s)
   

Proving Polynomial Identities

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

There are links between polynomials and geometry. Both branches of math use proof and a polynomial identity can be used to generate Pythagorean triples.

 
Favorites (5)
 
Resources (18)
 
Reflections (1)
pythagorean triplesresized
   

Review of Polynomial Roots and Complex Numbers

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

Arithmetic with polynomials and complex numbers are performed in similar ways, but powers of i have a meaning distinct from powers of variables.

 
Favorites (2)
 
Resources (10)
waterfall trivia
   

The Remainder Theorem

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

Any polynomial p(x) can be written as a product of (x – a) and some quotient q(x), plus the remainder p(a).

 
Favorites (3)
 
Resources (13)
 
Reflections (1)
remainder theorem exit
   

Quiz and Intro to Graphs of Polynomials

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

The graph of a polynomial can look a variety of ways depending on the degree, lead coefficient, and linear factors.

 
Favorites (3)
 
Resources (12)
 
Reflections (1)
quartic
   

The Lumber Model Problem

Algebra II » Unit: Cubic Functions
Algebra II » Unit: Cubic Functions
Jacob Nazeck
Fort Collins, CO
Environment: Suburban
 
Big Idea:

In many cases, polynomial functions are ideal mathematical models that support quantitative and abstract reasoning.

 
Favorites (3)
 
Resources (12)
 
Reflections (1)
800px logging in finnish lapland
   

Catch the Mistake

12th Grade Math » Unit: Midterm Review and Exam
12th Grade Math » Unit: Midterm Review and Exam
Tim  Marley
Troy, MI
Environment: Suburban
 
Big Idea:

Mathematical Practice 3 takes center stage as students critique the reasoning of others for problematic questions.

 
Resources (9)
untitled
   

The Dynamic Cubic Function

Algebra II » Unit: Cubic Functions
Algebra II » Unit: Cubic Functions
Jacob Nazeck
Fort Collins, CO
Environment: Suburban
 
Big Idea:

Using dynamic geometry software (GeoGebra) students intuitively understand the behavior of a cubic function.

 
Favorites (2)
 
Resources (20)
 
Reflections (2)
the dynamic cubic function
   

Seeing Structure in Expressions - Factoring Higher Order Polynomials

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

Like quadratic expressions, some higher order polynomial expressions can be rewritten in factored form to reveal values that make the expression equal to zero.

 
Favorites (5)
 
Resources (25)
 
Reflections (2)
factoring quick poll
   

Polynomial Long Division and Solving Polynomial Equations

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

Operations with polynomials are a lot like operations with integers.

 
Favorites (6)
 
Resources (22)
 
Reflections (1)
long
   

Higher Degree Polynomials, Day 1 of 2

Algebra II » Unit: Higher-Degree Polynomials
Algebra II » Unit: Higher-Degree Polynomials
Jacob Nazeck
Fort Collins, CO
Environment: Suburban
 
Big Idea:

Applying the Remainder Theorem and the Fundamental Theorem of Algebra, students explore the graphs of higher-degree polynomials.

 
Favorites (6)
 
Resources (12)
 
Reflections (1)
polynomialdeg4
   

The Fundamental Theorem of Algebra and Imaginary Solutions

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

The degree of a polynomial equation tells us how many solutions to expect as long as we include both real and imaginary solutions.

 
Resources (14)
 
Reflections (1)
quadratic imaginary
   

Cubic Equations Quiz

Algebra II » Unit: Cubic Functions
Algebra II » Unit: Cubic Functions
Jacob Nazeck
Fort Collins, CO
Environment: Suburban
 
Big Idea:

We've spent a long time practicing. Now it's time to demonstrate what you've learned!

 
Favorites (1)
 
Resources (9)
 
Reflections (1)
cubic image
   

The Factor Theorem & Synthetic Substitution

Algebra II » Unit: Cubic Functions
Algebra II » Unit: Cubic Functions
Jacob Nazeck
Fort Collins, CO
Environment: Suburban
 
Big Idea:

Synthetic substitution is an excellent tool that can be used strategically to help factor polynomials and identify zeros.

 
Favorites (3)
 
Resources (19)
 
Reflections (2)
synthetic substitution
   

Midterm Review Workshop

12th Grade Math » Unit: Midterm Review and Exam
12th Grade Math » Unit: Midterm Review and Exam
Tim  Marley
Troy, MI
Environment: Suburban
 
Big Idea:

Students work on midterm review and let you know what they still need help with.

 
Resources (3)
untitled
   

Arithmetic with Complex Numbers

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

Imaginary numbers are used to represent quantities that have two parts; working with these numbers is similar to working with polynomial expressions.

 
Favorites (5)
 
Resources (23)
 
Reflections (2)
mandlebrot set
Common Core Math
 
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