1. Characteristics of Polynomial Functions

2. Remember projectile motion… A quadratic is really a combination of different power functions

4. The path of marine animals… h(t) = t 4 + t 3 +…

6. What are the key features of graphs of polynomial functions?... TRACK: 1.End behaviour (D and R) 2.Number of minimum and maximum points. 3.Local minimum and maximum points 4.Number of x intercepts

7. See sheet…

8. We have been given a polynomial in graphical and algebraic form,… there is one more form we may see… A table of values….

9. A core part of all scientific research involves data collection…. The only way to write a general model of a relationship is to start by looking at a collection of specific cases

10. By looking at a graph, we can now attach a model. Is there a way to do it without graphing?....

11. A difference table can be used to analyze whether a given set of data points fits into a particular polynomial model.

12. Consider your summer job… Suppose you make $10/h HoursPay P ------ 10 – 0 = 10 20 – 10 = 10 30 – 20 = 10 40 – 30 = 10 0 0 101 202 30 3 404 Slope! Shows the rate of change (which is a constant!!) Once we find that constant rate of change, then we know how the function progresses from point to point…..

13. Consider y = x 2 + 1 XY Y Y 2 -3 --------------- -2-------- 0 1 2 3 10 5 2 1 2 5 -5 -3 1 3 5 2 2 2 2 2 The second difference is constant, so it must be a polynomial of degree 2!

14. Try y = x 3 + 1

15. Note: The sign of the constant difference term is also the sign of the leading coefficient. The leading coefficient “a” can be determined using the following formula. CD term = a[(n)(n-1)(n-2)(3)(2)(1), where n is the degree of the polynomial.

17. What type of polynomial?

18. Homework Pg 13 1 – 10 Harcourt Math 12: Ad Func and Intro Calc (yellow text)