HSF-IF.C.8

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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.8a

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- HSF-IF.C.8aUse the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
- HSF-IF.C.8bUse the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)t, y = (0.97)t, y = (1.01)12t, y = (1.2)t/10, and classify them as representing exponential growth or decay.

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## HSF-IF.C.8a

## Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

50 Lesson(s)

### Finding Roots of All Sorts

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### In this fast-paced lesson, students are introduced to as many ideas as they can handle, while also being given space to make their own sense of those ideas.

Favorites
(3)

Resources
(24)

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
(5)

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
(2)

Resources
(18)

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)

### Area Models for Multiplying Polynomials and Factoring Quadratic Expressions

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### This fast-paced lesson introduces multiplication of binomials and factoring of quadratic expressions for the first time, which sets students up to explore both in depth over the next few days.

Standards:

Favorites
(11)

Resources
(22)

Reflections
(1)

Big Idea:

#### Students make a list of perfect squares before keep a close watch to see where these special numbers pop up!

Standards:

Favorites
(4)

Resources
(21)

Reflections
(1)

### A Faster Way to Graph a Parabola

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### A neat but informally defined relationship between the roots and the vertex saves time now and lays foundations for a study of completing the square and the quadratic formula.

Standards:

Favorites
(2)

Resources
(18)

Reflections
(1)

### 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
(3)

Resources
(13)

### Finishing Five Point Graphs

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### A focus on special cases can reveal a lot about the fascinating behavior of quadratic functions.

Standards:

Favorites
(1)

Resources
(15)

Reflections
(1)

### More 4-Column Data Tables

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

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

Big Idea:

#### What happens when we remove the two middle columns? Students develop a method to solve problems with even less information given than the day before.

Standards:

Resources
(12)

### Profit Maximization

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

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

Big Idea:

#### What happens to the number of customers as you increase the price of the item? How does this affect your profit?

Standards:

Resources
(12)

### Quadratic Functions in Three Forms

Algebra I »
Unit: Quadratic Functions

Algebra I »
Unit: Quadratic Functions

Big Idea:

#### An brief adventure in number theory provides some background knowledge for completing the square, then students get to practice manipulating quadratic expressions in different forms.

Standards:

Favorites
(5)

Resources
(24)

Reflections
(3)

### Applying Data Tables to Word Problems

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

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

Big Idea:

#### Now that students have studied quadratic data patterns in depth, extend their understanding to word problems that require them to turn functions into equations.

Standards:

Favorites
(1)

Resources
(13)

### Investigating Profit with Products

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

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

Big Idea:

#### Look at a different type of problem-- one that has important similarities to and differences from the constant sum and difference problems -- to allow students to ask the question themselves.

Standards:

Resources
(12)

Reflections
(1)

### Quadratic Data Tables

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

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

Big Idea:

#### What properties of a quadratic function can be observed in a data table? How many data points on the graph of a quadratic function do you need to be able to find a function to fit the data?

Standards:

Favorites
(1)

Resources
(10)

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