##
* *Reflection: Problem-based Approaches
Introduction to Quadratic Functions - Section 1: Create a Foldable

Reflecting back on Common Core and the increased emphasis of mastering Quadratic Functions in Algebra I, I feel it is important for teachers to keep increasing rigor and relevance in our lessons. This lesson focuses on the parts and analyzing the graph of a Quadratic Function. An optional method to introduce Quadratic Functions is beginning with an application problem. A good application problem to begin with comes from this website, on page 21. It is a manufacturing problem that I model below. This website is the New York final assessment for math at:

http://gradnyc.com/wp-content/uploads/2013/04/FINAL-Math-HS-Functions-Unit-v2.pdf

Before graphing this problem with students, I have students create a Knows and Need to Knows column on their paper. I then randomly call on students to share out with the class.

In the Knows column, students list the following:

- The given function
- x is defined as number of units of the commodity sold
- R(x) is defined as revenue

An example of what students list in the Need to Know list is the following:

- What is revenue?
- What is commodity?
- Find maximum revenue
- Find the vertex
- Find the x and the y intercept(s)
- Explain the x and y intercept(s) in the context of the problem

Then we discuss next steps, which leads into graphing the function. This also provides a good opportunity to verify the answers by hand to review the Vertex Formula and the Quadratic Formula.

*Optional Introduction- Quadratic Function in Context*

*Problem-based Approaches: Optional Introduction- Quadratic Function in Context*

# Introduction to Quadratic Functions

Lesson 1 of 10

## Objective: SWBAT recognize the parts of a Parabola on the coordinate plane and the different forms of a Quadratic Function.

## Big Idea: Students create a foldable to help remember what key characteristics can be identified from a quadratic function in all three forms.

*50 minutes*

#### Create a Foldable

*15 min*

I introduce the students to the three different forms of Quadratic Functions with a foldable. I have students build a Foldable for Quadratic Functions using this blog post.

This blog can be found at the following website:

http://mathequalslove.blogspot.com/2014/03/different-forms-of-quadratic-function.html

(last accessed 6-09-15)

The foldable is in the bottom half of this page. I have students complete the 3 examples for the Quadratic Functions given in Vertex Form, Standard Form, and Intercept form. I also have students write down the notes with each one. I do not explain the different forms at this time. I want students to complete the foldable to refer back to in the next activity, and to use later in this unit.

*expand content*

#### Partner Activity

*30 min*

After the students have worked for 15 minutes on their foldable, I set up a Partner Activity for the students to interact with the objective. Students that have not completed their foldable in 15 minutes, I assign for them to complete it for homework. The Partner activity has two parts:

1. **To identify the Parts of the Parabola**

**a. Vertex (Max or Min)**

**b. Axis of symmetry**

**c. Zeros (roots, x-intercepts, solutions)**

**d. y-intercept**

**e. Direction of the Parabola**

**f. Domain and Range**

2. **To recognize a Quadratic Equation and the three different forms:**

**a. Standard Form**

**b. Vertex Form**

**c. Intercept Form**

**d. Quadratic but in none of the above forms**

For students to identify parts of the Parabola and key characteristics in **Part I**, I have students watch this short video. This video moves through the information quickly, so I pause it when necessary to point out key characteristics and to ask the students questions. Then I have students complete this online worksheet on their own paper to reinforce some of the concepts. Partners may complete the worksheet together. I expect this activity to take about 15 minutes for the students to complete and to review with the class.

For Part II of this activity, I show students different forms of Quadratic Equations using this Power Point. Students use a small whiteboard with their table partner to write their responses. When showing each slide, I have students first identify the form posted using the responses below of** A-E.**

**A. Standard Form**

**B. Vertex Form**

**C. Intercept Form**

**D. Quadratic but no certain form**

**E. Not Quadratic**

After students identify the form, we discuss as a whole class what can be identified about the parabola from the given equation with no work. We only discuss the characteristics that can be identified in the choices of **A-C**. Then we discuss what can be identified from the equation with a little work.

We discuss that the domain of any of the Quadratic Functions is all real numbers. The direction of any of the Parabolas in any form can be identified by the sign of **a**. The direction of the Parabola also determines if the Vertex is a Maximum or a Minimum. The Range depends on the Vertex and the direction of the Parabola. We discuss the characteristics listed below for each given form. Students continue to look at their foldable for the different formulas for each form.

- Standard Form- students recognize to identify the y-intercept as the constant of the given function. With a little work, students identify the formula to find the Vertex, but we do not find it at this time. I work with finding the Vertex from Standard Form in a later lesson.

- Vertex Form- students learn to identify the Vertex as (h,k) in the given formula on their foldable.

- Intercept Form- students focus on being able to identify the x-intercepts.

We briefly discuss that the other characteristics can be identified with a little work. However, this is an introduction lesson, and I emphasize only the characteristics that can be identified directly from the equation. The Vertex can be found in Vertex Form, and the x- intercepts can be identified in Intercept Form. In Standard Form, the constant is the y-intercept. I will focus on the other details in the next three lessons when we go into detail about each of the three forms.

*expand content*

#### Exit Slip

*5 min*

In this Exit slip I provide students a Parabola to analyze. I hand the Exit Slip to students with about five minutes remaining in the period. Students are to hand in the Exit Slip before leaving class. After analyzing the different parts of the Parabola, students are to write an equation for the Quadratic Function. I do not specify a certain form of the equation. I want students to use the parts that they have identified to decide which equation to write.

For example, using the vertex, students could write the equation in Vertex Form. Using the zeros, students can write the equation in Intercept Form. I do not expect students to master all of these concepts in this Introductory Lesson, but yet to start to make connections between the parts of the Parabola and the different forms of the Quadratic Functions.

*expand content*

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- UNIT 1: Introduction to Functions
- UNIT 2: Expressions, Equations, and Inequalities
- UNIT 3: Linear Functions
- UNIT 4: Systems of Equations
- UNIT 5: Radical Expressions, Equations, and Rational Exponents
- UNIT 6: Exponential Functions
- UNIT 7: Polynomial Operations and Applications
- UNIT 8: Quadratic Functions
- UNIT 9: Statistics

- LESSON 1: Introduction to Quadratic Functions
- LESSON 2: Graphing Quadratic Functions in Standard Form f(x)=ax^2+bx+c.
- LESSON 3: Graphing Quadratic Functions in Vertex Form f(x)=a(x-h)^2 + k.
- LESSON 4: Graphing Quadratic Functions in Intercept Form f(x)= a(x-p)(x-q)
- LESSON 5: Comparing and Graphing Quadratic Functions in Different Forms
- LESSON 6: Completing the Square of a Quadratic Function
- LESSON 7: The Quadratic Formula in Bits and Pieces
- LESSON 8: Solving Quadratic Functions Using the Quadratic Formula
- LESSON 9: Real World Applications of Quadratic Functions
- LESSON 10: Analyzing Polynomial Functions