Quadratic Functions: Standard and Intercept Forms

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SWBAT identify algebraic forms of quadratic functions and create accurate graphs of quadratic functions presented in standard and intercept forms.

Big Idea

Quadratic functions are graphed as parabolas; how we go about creating the graph depends on which form the function is written in.


15 minutes

Students will use Warm-up: Factoring Quadratic Expressions to practice factoring quadratic expressions as I check homework with the homework rubric.  While they complete the warm up, I show Desmos Quadratic in Standard Form on the overhead projector with the "a" animation turned on.  This will show the graph of a quadratic function that has the value of the lead coefficient changing gradually from -5 to 5 and back again.  Watching this animation helps students understand the role of the lead coefficient in changing the shape and orientation of a parabola.  If students do not ask about this animation, I will initiate a discussion about what is changing in the graph displayed on the overhead and how it is related to the algebraic representation of the function [MP2].  See the video, Using Desmos, for details about how I use Desmos to make connections between algebraic and graphical representations of quadratic functions.

If there are questions on the homework I will spend a few minutes answering them before we begin our discussion of standard and intercept form of quadratics.

Direct Instruction

20 minutes

I start our discussion of quadratic equations by asking students to turn to a table partner and brainstorm what they recall about quadratic functions.  Students tend to come up with many more ideas if they are allowed to brainstorm with a partner in this way before sharing with the whole group.  

I start the whole group discussion asking each group to share out something they recall about quadratic functions.  We take notes on standard, intercept and vertex forms of quadratic functions.  I describe these forms as "outfits" the function can wear, in the sense that the same function can be presented in 3 different ways.  Which form the function "wears" varies according to what we are using the function for [MP3].

After a general discussion of quadratic functions, we focus in on quadratic functions presented in standard and intercept forms.  I give students instructions in how to graph quadratic functions presented in these forms and how to convert a function written in one form to the other.  I provide example problems, which can be taken from WS Graphing Quadratic Functions in Standard and Intercept Forms. Throughout the discussion, I ask questions to engage students in the discussion and practice precise use of vocabulary [MP6].


40 minutes

With this introduction, students begin work on Exploring Quadratics - Standard and Intercept Forms.  This is a set of exercises in which students answer questions about quadratic functions and translate from algebraic to vebal and graphical representations of quadratic functions [MP2, MP7]. I take a few moments to review each section of the assignment and what is called for in the directions.  Students have an opportunity to ask questions about the assignment and then they work in their table groups to complete the problem set.  

As students work, I use the 3-Cup System to manage student frustration while providing a challenging experience for all students [MP1].  There may be times that I bring the whole group together to discuss something that is difficult for many students, but for the most part I prefer to answer questions at individual tables.  

Exit Ticket and Assignment

15 minutes

After 40 minutes of exploration, I bring students together for a discussion of the day's work.  I use Standard Intercept Quick Polls [MP5] to determine if students are able to identify key features of the graph by examining a quadratic function presented in standard or intercept form [MP7]. I pass out the problem set Graphing Quadratics in Standard and Intercept Forms, which will be the evening's homework.  Solutions to this set will be available on Edmodo and I remind students that they should check their work before arriving in class the following day.