Transformations on Quadratic Functions Day 1 of 2

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Students will be able to graph quadratic functions using transformations.

Big Idea

Use the area model of a quadratic function to explain why transformations work.

Warm up and Homework Review

10 minutes

I include Warm ups with a Rubric as part of my daily routine. My goal is to allow students to work on Math Practice 3 each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative specifically explains this lesson’s Warm Up- Transformations of Quadratic Functions Day 1, which asks students to describe the transformations on an absolute value function. 


Area Models for Transformations of Quadratic Functions

37 minutes

My goal for this lesson is to build the conceptual understanding of transforming quadratic functions which will enrich our future lesson on radical functions.  While this lesson straddles the line between Algebra 1 and Algebra 2 content, I feel like its connection as the inverse of radical functions enhances this unit enough to include it.  This lesson connects the area model of x2 with the graph of its function to allow students to visually understand WHY transformations do what they do (Math Practice 8).  We begin by looking at the area model, chart, and graph for f(x) = x2 which sets the base line for each transformation that we investigate.  I insist that students plot the vertex and the points one unit away on either side when graphing a quadratic because it will accurately show any stretches or shrinks (Math Practice 6).

The students then build the area model and graph  f(x) = ax2 when a  > 1, 0 < a < 1, and a < 0 (Math Practice 4).  The graphing calculator is used to confirm hypotheses about the effect of “a” on x2 and then the functions are sketched in their notes using the three points highlighted on the parent function. 

Finally, we then look at the transformation f(x) = x2 + b using a similar technique.

Detailed presentation notes are located in the PowerPoint.

Exit Ticket

3 minutes


Today's Exit Ticket asks students to draw an area model and graph a quadratic function.


This Assignment reaffirms the transformations learned in the day’s lesson.  There is a range of problems asking students to graph, write functions and draw area models given different sets of information.  The final problem extends the lesson by asking students to compare and contrast the graphs of a quadratic to a quartic function (Math Practice 7).