Standard Form of a Function

Standard Form of a Function

Form or written form of the relationship that defines a function and that highlights the parameters that transform the basic form of the function.

The standard form is a parametric form of a function rule in which the parameters characterize a transformation of the function’s graph.


The standard form that defines a second-degree polynomial function is:

f(x) = a(b(x – h))² + k

where the parameters h and k characterize the horizontal translation and the vertical translation, respectively, of the graph of the function associated with its basic form, and the parameters a and b characterize a vertical dilation and a horizontal dilation, respectively, of the graph associated with the basic form.

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