 State an equation for the following polynomial:

 End Behavior  Turns or “Bumps” for each polynomial  Investigate Roots

Leading CoefficientDegreeEnd Behaviors Positive Negative Positive Negative End BehaviorDegree Even Odd

 Polynomial solutions are made up of complex roots  A root is where the polynomial’s graph will intersect with the x-axis  A complex root describes two different types of roots: › Real Roots › Imaginary Roots (we will get to these next week)

 We classify the type of Real Root based on the degrees of each term and how it interacts with the x-axis.  Types: › Single Root › Double Root › Triple Root › And so on…

 Single Roots

 Double Roots

 Triple Roots

 Classify each type of root:

 What determines the number of turns the graph of a polynomial will have? › End Behavior › Degree of the Leading Term › Degrees of each factor, or the types of roots  The maximum number of turns a polynomial can have is (n-1) where n is the degree of the leading term

 On the worksheet from Thursday: › Describe the end behavior using the correct math notation › Circle each root on the graph. › Label each root as single, double or Triple.

 edscience/2013/10/600-grey-goblin.gif edscience/2013/10/600-grey-goblin.gif