Here are some notes that represent how I teach a unit on quadratics. (Watch out! My brain and approach is different!)

Algebra Module QUADRATICS _General Version

I start with the question:

Why the name quadratic? What does an expression of the form \(ax^2+bx+c\) have to do with the number four?

Answering this question reveals the power humankind discovered in using visuals and symmetry to solve equations. As such, I present teaching quadratics as about teaching the story of problem-solving and using symmetry to your advantage.

Once the algebra is in hand, graphing quadratics readily unfolds, as well as other bits and pieces: fitting quadratics to data, understanding parabolas and questioning whether all “U-shaped” graphs are quadratic, and the like. Those pieces are in the notes too.

[Actually: See the short course here on ARE ALL U-SHAPED GRAPHS QUADRATIC? if you are interested.]

For a full set of videos see a (very) full QUADRATICS COURSE here. 

The Quadratic Formula

Here are some rough-and-ready videos on the developing of the algebra of quadratics in a 21st-century thinking way. They are swift and scant on practice examples, but each video refers to a section in the notes which is chock full of proper details, loads of examples and practice problems, and all the solutions.

Bring in y0ur curriculum materials too and have a beautiful conversation with your students about how it all ties together.

Video 1 of 4: Pages 5-11 of the notes.

Video 2 of 4: Pages 12-18 of the notes.

Video 3 of 4: Pages 19-25 of the notes.

Video 4 of 4: Pages 26-35 of the notes.

Of course, feel free to continue working through the notes to see the symmetry approach to graphing, and more.

Enjoy!

p.s. And for those who want a real challenge, there is the mighty crazy CITADAUQ EQUATION one can try to make sense of too!

HIGHLY OPTIONAL EXTRA VIDEO

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