## 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.