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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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## Reader Reflections – April 2014

Readers comment on published articles or offer their own ideas.

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Readers comment on published articles or offer their own ideas.

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Readers comment on published articles or offer their own ideas.

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## Reader Reflections – April 2012

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## Sorting Out Ideas about Function

A card-sorting task can help students extend their understanding of functions and functional relationships.

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## Reader Reflections – March 2013

Readers comment on published articles or offer their own mathematical ideas.

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## Reader Reflections – April 2012

Readers react to published articles or submit their own mathematical explorations.