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Anna Clifford and JiWon Son
Solving quadratic functions is a cornerstone of first year algebra, but students struggle to gain a conceptual understanding of the process of completing the square. With the help of a historical perspective, students can gain both a deep geometric and algebraic understanding of the algorithm.
Douglas A. Lapp, Marie Ermete, Natasha Brackett, and Karli Powell
Algebra involves negotiating meaning between the worlds of mathematical ideas and the symbols that represent them. Here we examine classroom interactions and explorations as they relate to the connection of these worlds through the use of dynamically connected representations in a technologyrich environment.
Joe Garofalo and Christine P. Trinter
Students think resiliently about using the quadratic formula, analyzing factors graphically, finding the shortest distance between two points, and finding margin of error.
Leslie Dietiker
Research of enacted curriculum supports the role of sequence in framing lessons that are both coherent and interesting for students.
Michael Weiss
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 AREI.4b) and use the information learned from those methods to sketch the graphs of quadratic (and other polynomial) functions (CCSSM AAPR.3). More specifically, students learn to graph a quadratic function by doing some combination of the following:

Locating its zeros (xintercepts)

Locating its yintercept

Locating its vertex and axis of symmetry

Plotting additional points, as needed
Thomas G. Edwards and Kenneth R. Chelst
Connecting the formula to the graphic representation of quadratic functions makes the mathematics meaningful to students.
Readers comment on published articles or offer their own ideas.
Casey Hawthorne and Bridget K. Druken
Examples of solving equations and inequalities, analyzing quadratic expressions, and reasoning with functions show three ways to engage students in this mathematical practice.