Completing the Square

A polynomial function is of the form:



Important to note:

-the value of n must be a nonnegative integer (It must be a whole number, it is equal to zero, or it is a positive integer)

-the coefficients are These are real numbers.

The degree of a polynomial function is the highest value for n where is not equal to zero.

Determining the Degree of the Polynomial Function

Degree: 0
Name: constant

Degree: 1
Name: linear

Degree: 2
Name: quadratic

Degree: 3
Name: cubic

Completing the Square

Complete the Square:

Step One:

Put equation into Standard Form

Step Two:

Ignore the 7 for now and work with the equation...

Step Three:

Make a perfect square by diving 8 by 2 and squaring the new number and adding it to the equation. 

Step Four:

Simplify

Step Five:

You have added 16 to your original equation and therefore must subtract 16 to even it out. 

Step Six:

Add the 7 and simplify

Step Seven:

Solve for x.

Example:

Helpful Videos:

http://www.youtube.com/watch?v=gzm-uhj06q8&feature=related

http://www.youtube.com/watch?v=xGOQYTo9AKY