DO NOW 5/12/15 Identify the degree and leading coefficient of the following polynomials y = 3x3 – 2x + 7 y = -x4 + 3x2 – x + 8 y = 2x2 – 7x y = -x7 + x4 + 5x3 – 6x2 + x – 1 y = x + 4 y = -3x5 – 2x4 + 3x2 – 6x + 3

Happy Wednesday 5/13/15 Describe the end behavior of: f(x) = -5x8 – x6 + 7x + 5 Is the following a function? -15 + y2 + 3x = -9 + 7x

Intercepts and Turning Points 5/11/15 Objective: SWBAT determine the intercepts and number of turning points for a polynomial function https://www.youtube.com/watch?v=ajSkSUAYIdE

Zeros of Polynomial Functions For any polynomial function of degree n, the following statements are true The graph has at most, n – 1 turning points. (where the graph changes from increasing to decreasing) The function has at most, n solutions or x-intercepts Sometimes you can use the information about a graph to help find zeros, other times you can use the x-intercepts to help sketch a graph

Example Find the zeros of the function y = -2x4 + 2x2 and determine the number of turning points in the graph.

Example Find the zeros of g(x) = 2x2 – 3x + 1 and determine the number of turning points in the graph.

Example Find the zeros of the function y = 1/3x3 – 5x and determine the number of turning points in the graph.

Practice Find the zeros of each polynomial and determine how many turning points the graph will have. Describe the end behavior. f(x) = 49 – x2 f(x) = x2 + 10x + 25  f(x) = x3 – x2 – 6x

Graphs of Polynomial Functions To sketch a graph of a polynomial first identify the end behavior based on the degree Use the zeros of graph and the possible number of turning points to fill in the middle of the graph

Example Sketch a 2nd degree polynomial with the zero x = -2

DO NOW 5/14/15 Sketch a 6th degree polynomial with the zeros x = 0 and x = -5

Practice Sketch a 2nd degree polynomial with zeros at x = 2 and x = 4 Sketch a 3rd degree polynomial with zeros at x = -3, x = 0 and x = 1 Sketch a 3rd degree polynomial with zeros at x = -2, x = 4 and x = 7 Sketch a 3rd degree polynomial with the zero x = 9 Sketch a 4th degree polynomial with zeros at x = -5, x = 1 and x = 2 Sketch a 4th degree polynomial with zeros at x = -4, x = -1, x = 3 and x = 6 Sketch a 5th degree polynomial with zeros at x = -3, x = 1, x = 5 and x = 6 Sketch a 5th degree polynomial with zeros at x = -5, x = -1, x = 0 and x = 3

Practice Sketch a 4th degree polynomial with zeros at x = -5, x = 1 and x = 2 Sketch a 4th degree polynomial with zeros at x = -4, x = -1, x = 3 and x = 6 Sketch a 5th degree polynomial with zeros at x = -3, x = 1, x = 5 and x = 6 Sketch a 5th degree polynomial with zeros at x = -5, x = -1, x = 0 and x = 3