A parameter is a value that can be changed, that is not an independent variable.^{[1]} Usually, a parameter determines the form, but not the value of a function. For example, in the equation f(x) = ax, the parameter a determines the slope of the line. However, the value of the function is determined by the variable x.
A parameter is often used to define a family of functions. A family of functions is a set of functions that have similar properties. The family of linear functions is defined by the equation y=m(x-x_{1})+y_{1}. In this equation, m is the slope of the line, and (x_{1}, y_{1}) is a point on the line. Manipulative 1 shows how this works.
Click on the blue points on the sliders and drag them to change the figure. What type of line can not be described by this equation? Hint: It involves infinity. |
Manipulative 1 - Point Slope Form of a Linear Equation Using Parameters Created with GeoGebra. |
Another example of a family of functions defined by an equation using parameters is the equation y=a(x-x_{1})^{2}+y_{1}. In this equation a determines how wide or narrow the parabola is, and whether the parabola opens up or down. (x_{1},y_{1}) is the vertex of the parabola and x=x_{1} is the parabola's line of symmetry.
Click on the blue points on the slider and drag them to change the figure. |
Manipulative 2 - Equation of a Parabola with Parameters Created with GeoGebra. |
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