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Learning Cycle for Quadratic Transformations Utah Core Standards for Mathematics, Secondary II: Focus Standard: F.BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx) and f(x +k) for specific values of k (both positive and negative). Related Standards: F.IF.7, F.IF.9, F.IF.4 Develop Understanding Task: I am transformed. Discuss: Make note of the following mathematics as it arises in the presentations: In the context of quadratic transformations, participants will potentially: surface ideas such as . . . o o o o invent strategies to . . . o comparing horizontal and vertical representations to a function connecting transformation in real world situations to a function recognizing how the parent function changes as the situation changes (horizontally, vertically, stretched) understanding the definition of transformation match transformations to written functions and justify personal reasoning create representations that . . o demonstrate an understanding of creating a real world situation to a parent and its transformation. Purpose: The purpose of this task is for students to relate function notation to situations and to surface ideas about transformations. In Section I, these two expressions are similar in that they both involve adding 2. Look for students who give explanations that relate their knowledge about input and output and how these expressions would be impacted by the change given for each. Some examples may sound something like this: for f(h + 2), the 2 is added on the inside, so 2 feet is added to the horizontal distance. As a result, f(h + 2) gives the horizontal distance of 2 extra feet. Another example of what you might hear is that the expression f(h)+ 2 represents an outside change. We are adding 2 to f(h) or v, which represents the vertical distance the ball travels, not the horizontal distance. Therefore, f(h) + 2 means that we have 2 more vertical feet at any given horizontal moment. Solidify Understanding Task: Still Transforming This task solidifies the ideas surfaced in the I am Transformed document. Students will create their own context and explain the transformations. They will also create expressions that match situations and then sketch the corresponding graph. Practice Understanding Task: Features of Functions Participants will be given a parent function, and will graph the given transformation. They will also summarize the effect different transformations have on a function. Participants will: Use definitions and properties to… o Understand how the graph of the function will transform. o Synthesize knowledge about transformations into a table Use procedures to… o Graph the given transformation Create models that… o Represent the transformed function graphically o Confirm the definition of transformation