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Factored Form

Main Concept

Quadratic functions fx can be written in three forms.


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


axpxq     or     axp2


The parameters p and q are the roots of the function (the x-intercepts of the graph y=fx). 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:


a x2+b x+c


The parameter c is the y-intercept, while the parameter b 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, k and a constant, a times the square of a linear term:




The vertex of the graph is located at the point h, k. Converting a quadratic function to standard form is called completing the square.


In each case the parameter a determines the vertical stretching of the graph.


Choose the two roots of the parabola, and observe how the x-intercepts change to reflect each root.


a  =

p =

q =

Expanded form: 

Standard form: 

Factored form:

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