HSF-IF.C.7

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- HSF-IF.C.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
- HSF-IF.C.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- HSF-IF.C.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

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HSF-IF.C.7c

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- HSF-IF.C.7aGraph linear and quadratic functions and show intercepts, maxima, and minima.
- HSF-IF.C.7bGraph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
- HSF-IF.C.7cGraph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
- HSF-IF.C.7d(+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
- HSF-IF.C.7eGraph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

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## 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

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.

Standards:

Favorites
(4)

Resources
(18)

Reflections
(1)

### Review of Polynomial Roots and Complex Numbers

Algebra II »
Unit: Polynomial Theorems and Graphs

Algebra II »
Unit: Polynomial Theorems and Graphs

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.

Standards:

Favorites
(2)

Resources
(10)

### The Remainder Theorem

Algebra II »
Unit: Polynomial Theorems and Graphs

Algebra II »
Unit: Polynomial Theorems and Graphs

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).

Standards:

Favorites
(2)

Resources
(13)

Reflections
(1)

### Quiz and Intro to Graphs of Polynomials

Algebra II »
Unit: Polynomial Theorems and Graphs

Algebra II »
Unit: Polynomial Theorems and Graphs

Big Idea:

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

Standards:

Favorites
(3)

Resources
(12)

Reflections
(1)

Big Idea:

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

Standards:

Favorites
(3)

Resources
(12)

Reflections
(1)

### Catch the Mistake

12th Grade Math »
Unit: Midterm Review and Exam

12th Grade Math »
Unit: Midterm Review and Exam

Big Idea:

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

Standards:

Resources
(9)

Big Idea:

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

Standards:

Favorites
(2)

Resources
(20)

Reflections
(2)

### Seeing Structure in Expressions - Factoring Higher Order Polynomials

Algebra II »
Unit: Polynomial Theorems and Graphs

Algebra II »
Unit: Polynomial Theorems and Graphs

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.

Standards:

Favorites
(5)

Resources
(25)

Reflections
(2)

### Polynomial Long Division and Solving Polynomial Equations

Algebra II »
Unit: Polynomial Theorems and Graphs

Algebra II »
Unit: Polynomial Theorems and Graphs

Big Idea:

#### Operations with polynomials are a lot like operations with integers.

Standards:

Favorites
(5)

Resources
(22)

Reflections
(1)

### Higher Degree Polynomials, Day 1 of 2

Algebra II »
Unit: Higher-Degree Polynomials

Algebra II »
Unit: Higher-Degree Polynomials

Big Idea:

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

Standards:

Favorites
(5)

Resources
(12)

Reflections
(1)

### The Fundamental Theorem of Algebra and Imaginary Solutions

Algebra II »
Unit: Polynomial Theorems and Graphs

Algebra II »
Unit: Polynomial Theorems and Graphs

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.

Standards:

Resources
(14)

Reflections
(1)

Big Idea:

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

Standards:

Favorites
(1)

Resources
(9)

Reflections
(1)

### The Factor Theorem & Synthetic Substitution

Algebra II »
Unit: Cubic Functions

Algebra II »
Unit: Cubic Functions

Big Idea:

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

Standards:

Favorites
(2)

Resources
(19)

Reflections
(2)

### Midterm Review Workshop

12th Grade Math »
Unit: Midterm Review and Exam

12th Grade Math »
Unit: Midterm Review and Exam

Big Idea:

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

Standards:

Resources
(3)

### Arithmetic with Complex Numbers

Algebra II »
Unit: Polynomial Theorems and Graphs

Algebra II »
Unit: Polynomial Theorems and Graphs

Big Idea:

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

Standards:

Favorites
(4)

Resources
(23)

Reflections
(2)

Common Core Math

### Kindergarten

### First Grade

### Second Grade

### Third Grade

### Fourth Grade

### Fifth Grade

### Sixth Grade

### Seventh Grade

### HS Number & Quantity

### HS Algebra

### HS Functions

### HS Geometry

### Kindergarten

### First Grade

### Second Grade

### Third Grade

### Fourth Grade

### Fifth Grade

### Sixth Grade

### Seventh Grade

### Eighth Grade

### Ninth and Tenth Grade

### Kindergarten

### First grade

### Second grade

### Third Grade

### Fourth grade

### Fifth grade

### Middle School

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

HS Number & Quantity

HS Algebra

HS Functions

HS Geometry

Kindergarten

First Grade

Second Grade

Third Grade

Fourth Grade

Fifth Grade

Sixth Grade

Seventh Grade

Eighth Grade

Ninth and Tenth Grade

Kindergarten

First grade

Second grade

Third Grade

Fourth grade

Fifth grade

Middle School