Resources to Extend Thinking with Quadratics

 

Here are a few activities that I've used to extend thinking in our work with the Quadratic Function ...

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True False Statements Sorting Activity - Characteristics of Quadratics

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Odd One Out Activities give students opportunity to analyze, build vocabulary, and develop a discerning eye for mathematics.

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Partner Discussions or "He Said She Said" Activity asks students to analyze 2 problems, discuss them and then debrief.

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Always, Sometimes, Never statements are great for helping students think deeply about quadratics.

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Last ... Here is a collection of questions to promote critical thinking:

1) Write three different quadratic functions whose graphs have the line x = 4 as an axis of symmetry but have different y - intercepts.

2) The points (2, 3) and (-4, 3) lie on the graph of a quadratic function.  Explain how these points can be sued to find an equation of the axis of symmetry.
3) Write a quadratic function that has as roots, x = 2a and x = -5b.

4) For what nonzero whole number m does the quadratic equation x^2 + 3mx + (9/2)m = 0 have exactly one real solution for x?

5) What characteristics are most easily determined from a quadratic function written in standard form?  In factored form?  In vertex form?

6) The point (1, 5) lies on the graph of a quadratic function whose axis of symmetry is x = -1.  Your classmate says the vertex could be (0, 5).  Is your classmate correct?  Explain.