1. 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

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

3. Intercepts and Turning Points 5/11/15
Objective: SWBAT determine the intercepts and number of turning points for a polynomial function

4. 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

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

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

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

8. 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

9. 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

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

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

12. 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

13. 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