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Graphs in Search of Equations III

Module by: Interactive Mathematics Program

Intent

This is the third in a series of individual activities in which students develop their skill at finding equations for graphs of different types.

Mathematics

Students will be searching for equations for transformed quadratic functions of the form y = a(x + b)² + c. They will work from graphs and In-Out tables as they search for patterns.

Progression

Students will work on this activity individually and then share their results in a class discussion.

Approximate Time

20 minutes for activity (at home or in class)

10 minutes for discussion

Classroom Organization

Individuals, followed by whole-class discussion

Doing the Activity

The graphs in this activity may be more challenging than any that students have tried to identify up to now. Their work from Graphing Free-for-All and Graphing Summary should be helpful to them.

Discussing and Debriefing the Activity

Ask students to share the strategies they used to find an equation for each graph. They can use graphing calculators to check their equations.

If they are having difficulty, ask what familiar graph these graphs resemble (namely, y = x²)and how they differ from that graph. [link to math maps]

Key Questions

How are these graphs similar to and different from those in Graphing Free-for-All?

In what family of functions do these graphs fit?

What are the coordinates of the vertices of these graphs?

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