Polynomial Functions (Completing the Square)

Polynomial Functions:

Defined as in the form:



Restrictions:
- n must be a non negative integer
- Coefficiants must be real
- Powers of x must be whole numbers
- The degree of the polynomial is the greatest value of n (where )
- the domain of a polynomial is always all real numbers


Example of a Polynomial Function:

Converting from Standard Form to Vertex Form (Completing the Square):

Standard Form: 

Vertex Form:     

Start with the function 

Move aside the 15                                  

The goal is to turn            into a perfect square

To do so, we need to add 16. Normally this would be done by adding 16 to both sides, but because it is being shown as a function , we must add 16 and subtract 16 to the same side (equaling 0).

                                                    
                                                             
                                 

Example 1:


                   
          
                 



Example 2: