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.7a

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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.7a

## Graph linear and quadratic functions and show intercepts, maxima, and minima.

122 Lesson(s)

### Writing Linear Equations (Day 1 of 2)

Algebra I »
Unit: Linear & Absolute Value Functions

Algebra I »
Unit: Linear & Absolute Value Functions

Big Idea:

#### Students will analyze the different components of slope intercept form, and the purpose of each component in the entire equation.

Standards:

Favorites
(39)

Resources
(19)

Reflections
(2)

Big Idea:

#### Linear functions can be used to model how a changing quantity is represented in both the graph and equation of a function.

Standards:

Favorites
(10)

Resources
(16)

### Writing the Equation of A Linear Function (Day 2 of 2)

Algebra I »
Unit: Linear Functions

Algebra I »
Unit: Linear Functions

Big Idea:

#### This lesson allows students to understand how to use slope to write an explicit formula for a linear function.

Standards:

Favorites
(11)

Resources
(15)

### Building Connections: Building Polynomials (Day 1 of 2)

12th Grade Math »
Unit: Polynomial Functions and Equations

12th Grade Math »
Unit: Polynomial Functions and Equations

Big Idea:

#### Love, love, love(!) this lesson from NCTM where students build a polynomial function based on linear factors.

Standards:

Favorites
(8)

Resources
(23)

Reflections
(1)

### Review Workshop: Polynomial Functions and Expressions

Algebra II »
Unit: Polynomial Functions and Expressions

Algebra II »
Unit: Polynomial Functions and Expressions

Big Idea:

#### Tomorrow is the unit test on polynomial functions and expressions. In this lesson, we do more practice with word problems, solving equations, graphing parabolas, and rewriting quadratic functions.

Standards:

Favorites
(6)

Resources
(13)

Reflections
(1)

Big Idea:

#### Students finish up the Quadratic Functions Gallery Walk and begin to spot connections between where the roots and where the vertex are located.

Standards:

Favorites
(6)

Resources
(18)

Reflections
(1)

### What's In an Intersection?

Algebra I »
Unit: Systems of Equations

Algebra I »
Unit: Systems of Equations

Big Idea:

#### The "closeness" of one graph to another matches the accuracy of a guess and a check.

Standards:

Favorites
(2)

Resources
(16)

Reflections
(1)

### Quadratic Functions Review and Portfolio

12th Grade Math »
Unit: More Abstract Work with Quadratic Functions

12th Grade Math »
Unit: More Abstract Work with Quadratic Functions

Big Idea:

#### What are the key ideas and skills of this unit? What do you most need to review or understand better?

Standards:

Favorites
(1)

Resources
(7)

### What if We Start With the Axis of Symmetry?

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### An investigation of the relationship between the discriminant and the axis of symmetry lays foundations for students to understand the quadratic formula.

Standards:

Favorites
(2)

Resources
(26)

Reflections
(1)

### How Does a Parabola Grow?

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### It's not so much about the shortcut as it is about the structure it reveals!

Standards:

Favorites
(1)

Resources
(16)

Reflections
(1)

### Writing in Math Classroom, Part 1: Functions and Linear Functions

Algebra I »
Unit: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable

Algebra I »
Unit: Its Not Always a Straight Answer: Linear Equations and Inequalities in 1 Variable

Big Idea:

#### Students score sample MCAS open responses in groups as an entry point to understanding and reflecting on their own writing!

Standards:

Favorites
(1)

Resources
(15)

### Moving Toward Mastery: Completing the Square (Day 1)

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### There are uses for completing the square: first, as it relates to vertex form and graphing parabolas, and second as it relates to solving quadratic equations. Today, we'll get at both.

Standards:

Favorites
(3)

Resources
(28)

Reflections
(1)

### Moving Toward Mastery: Completing the Square (Day 2)

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### Students will continue to see that graphing quadratic equations and solving them work in tandem: the better we understand one, the more sense the other will make!

Standards:

Favorites
(1)

Resources
(15)

Reflections
(1)

Big Idea:

#### Starting with today's assignment, my classroom becomes a workshop. Every student will learn as much as they can between now and the end of the unit.

Standards:

Favorites
(3)

Resources
(17)

### Finding Vertices of Parabolas

12th Grade Math »
Unit: More Abstract Work with Quadratic Functions

12th Grade Math »
Unit: More Abstract Work with Quadratic Functions

Big Idea:

#### Why is finding the vertex of a parabola useful? How can you find the vertex when the function rule is written different ways?

Standards:

Favorites
(4)

Resources
(13)

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