## 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:

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

Lesson 1 of 10

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

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Subject(s):
quadratic functions, Math, Quadratic Equations, standard form, axis of symmetry, foldable, 3 forms, vertex form, Intercept Form, vertices, Maximum and Minimum
50 minutes

### Rhonda Leichliter

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