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Parameters, Sliders, Marble Slides, Oh My!

Three different technological activities to explore parameters of quadratic functions each has its own pros and cons.

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Visualizing Complex Roots of a Quadratic Equation

A quadratic equation was the basis for activities involving both concrete and technological representations.

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Linking Factors and Multiples to Algebraic Reasoning

In this paper we illustrate how a task has the potential to provide students rich explorations in algebraic reasoning by thoughtfully connecting number concepts to corresponding conceptual underpinnings.

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Solving and Graphing Quadratics with Symmetry and Transformations

One of the central components of high school algebra is the study of quadratic functions and equations. The Common Core State Standards (CCSSI 2010) for Mathematics states that students should learn to solve quadratic equations through a variety of methods (CCSSM A-REI.4b) and use the information learned from those methods to sketch the graphs of quadratic (and other polynomial) functions (CCSSM A-APR.3). More specifically, students learn to graph a quadratic function by doing some combination of the following:

• Locating its zeros (x-intercepts)

• Locating its y-intercept

• Locating its vertex and axis of symmetry

• Plotting additional points, as needed

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Conic Connections with Polar Functions

Encourage investigation of the conic-section attributes of focus, eccentricity, directrix, and semi-latus rectum using polar coordinates and projective geometry.

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Happy Families, Continued

Explore the relationship between families of quadratic expressions factorable over the integers and Pythagorean triples.

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Readers comment on published articles or offer their own ideas.

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