Main Concept

Quadratic functions  can be written in three forms.

Factored form, the product of a constant and two linear terms:

     or     

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.

a  =

p =

q =

Expanded form: 

Standard form: 

Factored form: