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State an equation for the following polynomial:

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

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Leading CoefficientDegreeEnd Behaviors Positive Negative Positive Negative End BehaviorDegree Even Odd

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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)

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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…

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Single Roots

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Double Roots

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Triple Roots

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Classify each type of root:

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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

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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.

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http://www.wired.com/images_blogs/wir edscience/2013/10/600-grey-goblin.gif http://www.wired.com/images_blogs/wir edscience/2013/10/600-grey-goblin.gif

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Quadratic Theory Introduction This algebraic expression: x 2 + 2x + 1 is a polynomial of degree 2 Expressions like this in which the highest power of x.

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