Authentic Lessons for 21st Century Learning

Transformers Part 1: Absolute Value and Quadratic Functions

Function Transformations

K20 Center, Michell Eike, Erin Finley, Kate Raymond, Melissa Gunter | Published: June 8th, 2022 by K20 Center

  • Grade Level Grade Level 9th, 10th, 11th
  • Subject Subject Mathematics
  • Course Course Algebra 1, Algebra 2
  • Time Frame Time Frame 2-3 class period(s)
  • Duration More 120 minutes

Summary

Students will use a graphing tool to analyze basic transformations on a variety of parent graphs in order to create general rules about function transformation.

Essential Question(s)

What are parent graphs? How are the transformations of parent graphs related? What are the general rules for transformations of a parent graph?

Snapshot

Engage

Students begin their exploration of function transformations by analyzing linear functions, with which they should already be familiar.

Explore

Small groups of students are provided a handout which guides them through the exploration of transforming absolute value and quadratic functions in order for them to generalize the transformation rules.

Explain

Students come to consensus on the general transformation rules in a class discussion.

Extend

Students are allowed to create their own graphs and equations, before switching with another group to determine the corresponding equations or graphs.

Evaluate

Students are provided with an opportunity to generate the corresponding graphs for given equations, and then the corresponding equations for given graphs.

Materials

  • Notebook paper

  • Pencil

  • Desmos Studio

  • Exploring Graphs (attached; one per student)

  • Lesson Slides (attached)

  • Projector screen/Document camera or other way to display information

Engage

15 Minute(s)

Introduce the lesson using the attached Lesson Slides. Slide 3 displays the lesson’s Essential Questions: What are parent graphs? How are the transformations of parent graphs related? What are the general rules for the transformation of parent graphs? Slide 4 identifies the lesson’s learning objectives. Review each of these with your class to the extent you feel necessary.

Before starting the activity, have students pick a partner. Students need a graphing calculator or access to desmos.com to complete the activity. Go to slide 5 and display the equations y = x, y = 2x, and y = ½x for the students. Have the students use the graphing calculator to graph each function and ask them to compare and contrast the resulting graphs. Using Think-Pair-Share, have students share their answers. Choose a few students to share with the class.

Go to slide 6 and pose the same question using y = x + 1, y = x – 2, and y = x + 3. Discuss how these changes resulted in different graphs than the previous ones.

Discuss with students the idea of a parent graph.

Explore

45 Minute(s)

Go to slide 7 and have students continue to work with their partner to complete the attached Exploring Graphs handout. Allow students to work in their pairs independently but monitor their progress.

Students need a graphing calculator or access to desmos.com to complete the activity. Students should make predictions about graphing and comparing y = |x|, y = |x-1|, y = |x+3|, y = |x| - 2, and y = |x-2| + 3. Students do this again, but with quadratic functions: y = x², y = (x-3)², y = (x+1)², y = x² + 4, and y = (x-2)² + 3.

Students are asked to compare their absolute value and quadratic graphs to list observations and patterns.

Each group then joins another group to compare what they observed.

Explain

25 Minute(s)

Go to slide 8 and have students share out what they observed from the Exploring Graphs handout with the class.

  • What were the changes to the absolute value function?

  • What were the changes to the quadratic function?

  • What are the general rules of transformations?

Make sure there is consensus on the transformation general rules.

Extend

25 Minute(s)

Go to slide 9 and have students create their own graphs and equations in pairs to trade with another pair. Have students work with their original group to create:

  • 1 absolute value equation (no graph)

  • 1 absolute value graph (no equation)

  • 1 quadratic equation (no graph)

  • 1 quadratic graph (no equation)

Then have groups trade their creations with another group. Each group now needs to find the missing graph and equation for each provided equation and graph.

Evaluate

10 Minute(s)

Go to slide 10. Using Think-Pair-Share, have students predict how the graph of y = -|x+3| - 5 would differ from the parent function.

Resources