Review Preview What is the degree of the following Polynomials? 𝑓 𝑥 = 2𝑥 2 −4 𝑥 6 +8𝑥 𝑓 𝑥 = −4𝑥 3 +2𝑥−3 List each zero and its multiplicity. 3. y=(𝑥+2) 𝑥−3 2 (𝑥−4) 4. 𝑓 𝑥 = 𝑥+7 3 (𝑥−2)

U5D2 Polynomial functions January 4th, 2016

Turning points Turning points are the points on the graph where the graph changes from increasing to decreasing, and vice versa. Example: Graph 𝒙 𝟑 −𝟐 𝒙 𝟐 to determine its turning points *** A polynomial of degree n has at most n-1 turning points. Similarly, if the graph has n-1 turning points, the polynomial is at least n. Example: how many turning points will a cubic function have? A quartic? If a polynomial has 5 turning points, it must be of what degree?

How many turning points will the graph 𝑓 𝑥 =3(𝑥−7) (𝑥+3) 2 have? You try! How many turning points will the graph 𝑓 𝑥 =3(𝑥−7) (𝑥+3) 2 have?

Example: What is the end behavior of 𝒇 𝒙 = 𝒙 𝟐 𝒙−𝟐 ? Where is the graph “traveling” to? Definition: For large values of x, either positive or negative, the graph of the polynomial resembles the graph of the power function. Example: What is the end behavior of 𝒇 𝒙 = 𝒙 𝟐 𝒙−𝟐 ?

Graphing Polynomial Functions Graph 𝑓 𝑥 = 2𝑥+1 𝑥−3 2 . What are the zeros? What is the domain and Range? What are the Intervals of Increase And Decrease? What is the End Behavior?

Graphing Polynomial Functions Graph 𝑓 𝑥 = 𝑥 2 (𝑥−2)(𝑥+2). What are the zeros? What is the domain and Range? What are the Intervals of Increase And Decrease? What is the end behavior?

Classwork: Pg. 189: #s 65-67 Graph, List the zeros, domain and range, intervals of increase and decrease, and end Behavior.

homework Graph, find the zeros, state the domain and range and intervals of increase and decrease, and the end behavior 𝑓 𝑥 = 𝑥+1 𝑥−2 𝑥+4 𝑓 𝑥 = 𝑥 2 𝑥−3 (𝑥+4)