Reflection: Student Led Inquiry Building Quadratic Functions: f(x), kf(x) and f(kx) - Section 2: Collaborative Project: Manipulating Quadratic Functions


I love this lesson as it allows students to explore different manipulations of functions (adding a constant and multiplying by a constant, for example) and hits a nice balance of focus, structure and flexibility. As the Student Work shows, I try to have students start with the details and create equations and complete the table to write down observations and notes on the effect of, for example, adding 4 to the function x^2.

The student work examples attached to this reflection demonstrate various levels of understanding, but asking students to generalize/identify patterns they see form their observations is an important skill. Analyzing notes and observations to identify overarching themes and patterns is a skill that will support student learning in math, English, Science and almost any other discipline they choose to engage in. 

This activity is also a great example of the math practice standards MP.3 and MP.8  in action. Working in pairs in this scaffolded activity encourages students to critique each other’s reasoning. The specific task also asks students to see regularity in repeated reasoning – as they look at different graphs of specific functions they are looking for repeated patterns in order to make generalizations of the effect of k on f(x) for each of the three scenarios.

  Student Led Inquiry: Investigation as an Inquiry Tool to Understanding Quadratics
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Building Quadratic Functions: f(x), kf(x) and f(kx)

Unit 7: Interpret and Build Quadratic Functions and Equations
Lesson 6 of 13

Objective: SWBAT use technology to identify the effect on a graph of replacing f(x) with f(x) + k, k*f(x), and f(k*x).

Big Idea: Students use technology to construct their own understanding of different operations on the graph of quadratic functions!

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exit ticket manipulating quadratics
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