A parameter is a value that can be changed, that is not an independent variable. 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 - x1) + y1. In this equation, m is the slope of the line, and (x1, y1) 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 - x1)2 + y1. In this equation a determines how wide or narrow the parabola is, and whether the parabola opens up or down. (x1, y1) is the vertex of the parabola and x = x1 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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