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Internet Resources for the Calculus Student - Topics in Precalculus

Quadratic Functions

Functions of the form f(x)=a*x^2+b*x+c are called quadratic functions beacuse they involve the second power or square of the variable, and "quadratus" was the latin word for a square. Such functions arise in applications whenever we are interested in the product of a pair of linearly related quantities.

You can (if equipped with one of the latest Java-enabled browsers - preferably with Sun's new plug-in for Java) use our Graph Explorer to see the effects of changing the parameters. (Any Computer Algebra System or Graphing Calculator would do as well of course but the detailed instructions might be a bit different.) You can also enter a quadratic as a product of linear factors and then also graph the factors separately to see how the x-intercepts of the product are related to those of its factors.

For guidance through a more detailed exploration you can work through our on-line lab on
Quadratic Functions.

This "game" has you choose the coefficients a,b, and c to make the graph of y=a*x^2+b*x+c match a given parabola.

Here are some more links to material on quadratic functions:

Completing the square(1)(@ArkansasStU)
Completing the square(2)(@ArkansasStU)
Quadratic formula - derivation(@ArkansasStU)
MathsOnlineGallery (@uVienn.austria) - Quadratic Eqns
Problem of Quadratic Functions (1)@ies
Problem of Quadratic Functions (2)@ies
Problem of Quadratic Functions (3)@ies
Minimum Value of Quadratic Functions@ies
Vertex of a quadratic curve(@ArkansasStU)

MathsOnlineGallery (@uVienn.austria) SimpleMaxAreaProblem
StudyWeb -Math - Quadratic Equations

 If you have come across any more good web-based illustrations of these and related concepts,
     please do let us know and we will add them here.

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