1. Graphs of Polynomial Functions

2. Parent Graphs  Quadratic Cubic Important points: (0,0)(-1,-1),(0,0),(1,1)  QuarticQuintic  (0,0) (-1,-1),(0,0),(1,1)

3. Click on the graph below to connect to an interactive page.

4. Turning Point – Point on the graph such that the value of the function is a relative maximum or a relative minimum. A graph of a polynomial of degree n can have as many as n-1 relative extrema. Leading Coefficient – coefficient of term with the highest degree. If a is positive, and If n is even, both left and right sides of the graph . If n is odd, the left side , and the right side . If a is negative, and If n is even, both left and right sides of the graph . If n is odd, the left side  and the right side . degree

5. Click on the graph below to connect to an interactive page.

6. EVEN function : f(  x) =f(x) ; symmetric about the y-axis. ODD function: f(  x)=  f(x) ; symmetric about the origin. even odd How many relative extrema does each graph have?

7. Click on the graph below to connect to an interactive page.

8. What is the equation of the graph? 1 st : the shape is cubic and positive The factors are (x+1), x and (x-2). So, the equation must be : 2nd : there are zeros at –1, 0 and 2   How many relative extrema?

9. What is the equation of the graph?

11. What is the shape of the graph of an even polynomial equation with a degree of 4, a negative leading coefficient and 2 distinct real zeros?

12. What is the shape of the graph of the polynomial equation of degree 5 with a positive leading coefficient and 5 distinct real zeros?

13. Graph without a calculator:

14. **If (x-r) is a factor k times, then r is a zero of multiplicity k. That zero is a touch point (point of tangency) if its multiplicity is an even number. (It will not cross the x-axis at that point.) Graph: If the multiplicity is odd and > 1, the graph will flatten out as it crosses the x-axis.

15. Click on the graph below to connect to an interactive page.