Family of Functions
This applet is designed to allow a visual exploration of a family of function, or how shifting a parameter changes the graph.
The applet opens with the function f(x) = a*x^2 + b*x + c.
The sliders on the side let you change the parameters.
To change the function, right-click (control-click for mac
people) on the formula and choose "redefine" from the context menu that
pops up. To change the viewing area, right-click on bank
space in the graphing pad and choose "properties".
Mike May, S.J., 2/18/2006, Created with GeoGebra
Some interesting families of curves to examine:
- The first example graphs quadratic functions. They can be expressed in a numebr of ways, each of which has advantages:
- The general format -- f(x)=a*x^2+b*x+c - Nice polynomial format - Geometric understanding of parameters hard.
- Vertex format -- f(x) = a*(x-b)^2+c - The parameters give the vertex and direction.
- Intercept format -- f(x) = a*(x-b)*(x-c) - the parameters give the x intercepts.
- Linear combinations of sin(x) and cos(x) -- f(x) = a*sin(x) + b*cos(x)
- Logrithmic curves -- f(x) = a*log(b*x^c)
- Rational functions -- f(x) = (x*(x-a))/((x-b)*(x-c))
GeoGebra is a GNUed software package for mathematics visualization.
The home for the applications is http://www.geogebra.org.
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Last updated By Mike May, S.J., September 23, 2007.