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These lessons include the core of an Algebra 2 unit, plus some material for high school math teachers.
- A manipulatives-based complement to this work (or to any work on quadratics) can be found in my book Lab Gear Activities for Algebra 1 (where to get it.) The manipulatives make factoring and completing the square accessible to the vast majority of Algebra 2 students, while giving them a geometric perspective which is unfortunately missing from many curricula.
- See an applet that presents a compatible but continuous view of completing the square.
- See also a sample activity from the end of the book, which makes a connection between the Lab Gear and graphical representations of certain quadratics (PDF).
- An application of quadratic functions, from my book Algebra: Themes, Tools, Concepts:
- Maximizing Area | Condensed version.
- The lessons below (in PDF format) involve the sparing use of the graphing calculator. Unlike some other calculator-based approaches ("graph this, graph that, what do you notice?") this is a rather theoretical unit, which helps develop students' symbol sense and goes for a lot more depth of understanding than is customarily expected at this level.
- Factored Form of Quadratic Functions | Applet
- From Factored to Standard Form
- Moving Parabolas Around
- Quadratic Forms (a condensed version of the above three lessons, probably better suited for teachers)
- Make These Parabolas: TI-83/84, TI-89
- Quadratic Parameters
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This lesson derives the quadratic formula in a straightforward way based on this approach, an alternative to completing the square:
- A Graphical Approach to the Quadratic Formula
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This lesson for teachers (and perhaps precalculus students) presents a brand new proof of the quadratic formula which involves neither parabolas nor completing the square:
- A Different Approach to the Quadratic Formula
- (background: Constant Sums, Constant Products)
- A related Cabri applet
Another presentation of some the above material appeared as an article in the February 2008 issue of The Mathematics Teacher, under the title "A New Path to the Quadratic Formula".
- Parabolas are a major topic in secondary school, and yet in the US, students and teachers do not often think about them as geometric objects. This may be a consequence of the strict division between algebra and geometry courses. As a result, many basic properties of parabolas are not well understood. These pages present some key concepts in this domain:
- Geometry of the Parabola: 2D | 3D
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