What?! Polynomial Functions has its Family?

In a family, we have some similarities with our parents and siblings and other relatives. It can be the physical appearance or the characteristic. Same goes to the Polynomial equation of a family! I know, you might think what I am talking about absolute ridiculous rubbish. Hahaha~ chill~


First of all, let me explain what is the families of polynomial functions. A polynomial function that belongs to a family have the same characteristic. Polynomial function of the same family have the same x-intercept, roots, and zeros.


Example:


f(x)=(x+1) (x-1) (x+3) and
f(x)=2(x+1) (x-1) (x+3) 
belong to the same family because they have the same x-intercepts, roots and zeros. 


Example 2: 

Three polynomial equations above are of the same family because they have the same x-intercept of 2 and 5.


To determine the equation of the particular member of the family, the only thing that we require is any one point on the graph. We can substitute the x value or y-value into the function and find out the variable that differs the shape of the graph.


In general, polynomial functions of the same family can be represented in the form, 


y = k( x - a₁ ) ( x - a₂ )...( x - an ), where k ∈ R, k ≠ 0.

Birds of a feather flock together. 
Polynomial equation of a family, share the same x-intercept together. 




See? I told you polynomial functions have their own family. Haha! Enjoy~


Web resource:The Family of Quadratic Functions <http://www.glencoe.com/sec/math/algebra/algebra1/algebra1_08/other_calculator_keystrokes/472_Alg1_9-1B_873823_CFX.pdf>