Quadratic functions can be written in three forms.
Factored form, the product of a constant and two linear terms:
The parameters and are the roots of the function (the x-intercepts of the graph ). Converting a quadratic function to factored form is called factoring.
Expanded form, a sum of terms, each of which may be a product of a constant and some variables:
The parameter is the y-intercept, while the parameter is the slope of the tangent at 0. Converting a quadratic function to expanded form is called expanding.
Standard form, the sum of a constant term, and a constant, times the square of a linear term:
The vertex of the graph is located at the point . Converting a quadratic function to standard form is called completing the square.
In each case the parameter determines the vertical stretching of the graph.