MIT Massachusetts Institute of Technology

The Quadratic Equation: It’s Hip to Be Squared

Gilbert Strang
Professor of Mathematics
Massachusetts Institute of Technology
Cambridge, Massachusetts 02139 USA

The Portuguese Subtitle video has been broken into two parts, you can view:
Part 1 Portuguese Subtitle | Part 2 Portuguese Subtitle

This lesson aims to help students with quadratic functions y = ax2 + bx + c. This is the next step after linear functions bx + c. The lesson begins with three quadratics and their graphs (three parabolas):  y = x2 - 2x + (0 or 1 or 2). The prerequisite or co-requisite is some working experience with algebra, like factoring x2 -2x into x(x-2). The objective is to connect four things: the formula for y, the graph of y (a parabola), the roots of y and the minimum or maximum of y. The particular example y = x2 – 2x could be repeated by the teacher, for emphasis. The lesson will take more than one class period (and this is deserved!). The breaks allow time to consider parabolas starting with -x2  and opening downward. A physical path would be one (dangerous?) activity.

Professor Strang teaches Linear Algebra and Computational Science at MIT, and both of these classes are videotaped and available on MIT's OpenCourseWare ocw.mit.edu. He also writes research papers and textbooks on these subjects. Click here to read more about Professor Strang.

This is a link to Professor Strang’s video, Introduction to Calculus. The first section entitled “The Big Picture” should be particularly helpful.
http://www.youtube.com/watch?v=X9t-u87df3o

At this site you will find all the Khan Academy videos on the quadratic equation.
http://www.khanacademy.org/search?page_search_query=quadratic+equation

This site, sponsored by +Plus magazine, presents an article entitled “101 Uses of the Quadratic Equation”.
http://plus.maths.org/content/101-uses-quadratic-equation

This site, sponsored by +Plus magazine, presents an article entitled “101 Uses of the Quadratic Equation Part II”.
http://plus.maths.org/content/101-uses-quadratic-equation-part-ii

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