Factored Form - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim

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:

More MathApps