## Unit 6

MODELING AND ANALYZING QUADRATIC FUNCTIONS

**UNIT DESCRIPTION**

In this unit, students analyze quadratic functions and their characteristics. They rewrite and interpret equivalent forms of quadratic expressions and equations in order to expose important characteristics and analyze those characteristics to solve problems. Students learn to anticipate the graph of a quadratic function by interpreting various forms of quadratic expressions and equations. They identify the real solutions of a quadratic equation as the zeros of a related quadratic function. Students will use different techniques to solve quadratic equations including taking square roots, factoring, completing the square, and using the quadratic formula. They use their understanding of mathematical modeling to build functions that can be used to explain quadratic phenomena, and to compare functions represented in different ways. In the scope of this course, students only work with real number solutions.

**LEARNING TARGETS**

- I can graph quadratic functions from different forms (vertex, standard, intercept) to highlight key features
- I can identify transformations of quadratic functions in vertex form
- I can identify characteristics of quadratic functions
- I can identify quadratic relations as functions and determine the domain and range from real world scenarios
- I can compare rates of change between linear, exponential, and quadratic functions
- I can add and subtract polynomials
- I can multiply polynomials (monomial and binomial and two binomials to produce a quadratic expression)
- I can factor a quadratic expression.

**TEXTBOOK CONNECTIONS**

**Module 3**Lesson 2- Functions: Students determine if a relation is a function and find function values.

Lesson 3- Linearity and Continuity of Graphs: Students identify linear and nonlinear functions and continuous and discrete functions.

Lesson 5- Shapes of Graphs: Students identify symmetry, extrema, and end behavior of functions.

Lesson 6- Sketching Graphs and Comparing Functions: Students sketch graphs of functions and compare two or more functions.

**Module 4**Lesson 2- Rate of Change and Slope: Students find and interpret the rate of change and slopes of lines.

**Module 9**Lesson 1- Exponential Function: Students graph exponential functions.

**Module 10**Lesson 4- Special Products: Students multiply binomials by applying special patterns.

Lesson 5- Using the Distributive Property: Students factor polynomials by using the Distributive Property.

Lesson 6- Factoring Quadratic Trinomials: Students factor trinomials into two binomials.

Lesson 7- Factoring Special Products: Students factor polynomials by applying special patterns.

**Module 11**Lesson 1- Graphing Quadratic Functions: Students analyze and graph quadratic functions.

Lesson 2- Transformation of Quadratic Functions: Students identify the effects of transformation of the graphs of quadratic functions.

Lesson 3- Solving Quadratic by Graphing: Students write quadratic equations and solve them by graphing.

Lesson 4- Solving Quadratic Equations by Factoring: Students solve quadratic equations by factoring and by using the Square Root Property.

Lesson 5- Solving Quadratic Equations by Completing the Square: Students solve quadratic equations by completing the square.

Lesson 6- Solving Quadratic Equations by Using the Quadratic Formula: Students solve quadratic equations by using the Quadratic Formula.

Lesson 8- Modeling and Curve Fitting: Students model data with linear, exponential, and quadratic functions.

**IXL SKILLS**

__Graphing:__

- Complete the table: CC.3
- Graphing: CC.5, CC.14 (standard form), CC.17 (enrichment)

__Transformations:__

- CC.4, CC.15
- Standard to Vertex: CC.15
- Vertex to Standard:

__Characteristics:__

- Characteristics: CC.1, CC.2
- Domain and Range: CC.16

__Polynomial Operations:__

- Adding/Subtracting: AA.1, AA.4, AA.5
- Multiplying: AA.6, AA.8, AA.9, AA.11, AA.12

__Factoring Quadratics:__

- BB.1-2 (GCF), BB.4-5 (Trinomials), BB.6 (Difference of Squares), BB.7 (Factor by Grouping), BB.9 (Mixed Review)

__Solving Quadratics:__

- Solving by Square Roots: CC.6
- Factored Form: CC.7, CC.8
- Completing the Square: CC.9, CC.10
- Quadratic Formula: CC.11, CC.12 (Discriminant)