The Discriminant: the Inside Scoop of the Quadratic Equation

Discussing the discriminant separately from the Quadratic Formula is an important part of any discussion of solving quadratic equations.  By letting students discover for themselves the relationship between the value of the discriminant and the number of roots of a quadratic equation, students learn the importance of the concept of the discriminant, and are more likely to evaluate the discriminant separately.  They will then be less likely to 'lose the sign' of the discriminant, and find erroneous roots for equations that have no roots.

If you wish to have your students use this webquest, you must already have shown the derivation of the quadratic formula, and have labeled the three major parts of the quadratic formula, as follows:

The quadratic divisor, which is 2a.

The linear term, which is -b.

The discriminant, which is b²-4ac.

Set your students about this task either as a homework assignment, or, if you have sufficient internet devices available in your classroom, as a think-pair-share investigation.  If students appear to be having difficulty successfully answering the quiz questions, especially in the think-pair-share environment, suggest they start with the simpler examples, x²=0 and x²-1=0, which should already have been solved in a prior lesson.

You may also wish to route students to the Wikipedia page on the quadratic formula:
http://en.wikipedia.org/wiki/Quadratic_equation
Wikipedia is an excellent resource for mathematical content; despite the reputation as unreliable, since anyone may post without citing resources, Wiki's math articles are explicit, highly rigorous, usually accompanied by diagrams, and go deeper than most other sites.   Whenever I need a further explanation of a mathematical concept, and do not have a university professor handy, I go to Wikipedia first.