Introducing Quadratic Functions

Aside from all things trigonometry, quadratic functions are my favorite. I instantly feel old when I stop long enough to ponder the number of lessons in my classroom that have involved quadratic functions. But I'm always open to new ideas, so I hope this Genius Hour series will prompt robust discussion.

Let's start with a broad overview. Now...there are several schools of thought on building the concept of quadratic functions. You will spy an overarching theme in the quadratic functions progression below...a deep understanding of the behavior of quadratic functions which enables students to make connections within any quadratic function model.

Quadratic Functions At-A-Glance:

• Graphing Quadratic Functions in Vertex Form
• Identifying Key Characteristics from Vertex Form
• Applications in Vertex Form (includes connections to key features)
• Generating Standard Form from Vertex Form (includes operations of polynomials)
• The Pros and Cons of Vertex Form and Standard Form (includes solving by square roots)
• Rewriting Standard Form in Vertex Form and Intercept Form (includes solving by completing the square and factoring)
• Generalizing the Solving Process...Deriving the Quadratic Formula (includes finding the vertex from standard form, nature of the roots via the discriminant, and imaginary solutions)
• Applications in Standard Form (includes connections to key features)

I'm not just partial to quadratics. When I teach any function, my ongoing thread is transformations of the parent function. And since the graph provides a great visual to aid in the discovery of key features necessary for application, let's start with graphing quadratic functions. Browse the Puzzle Challenge, Geometric Discovery, Mr. Norm Parabola Narrative (or an alternate Parabolic Graphing Transformations Lab Activity), and a "Go Fish!" Quadratics Matching Game and coordinating Find the Vertex Practice Set to jumpstart your planning for building the concept of quadratic functions.

Introduction to Quadratic Functions

This introduction set highlights Common Core State Standards HSF-IF.B.4 and HSF-IF.C.7a included in 7th and 8th Accelerated Algebra 1.