Characteristics of Polynomial Functions

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

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

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

See sheet…

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

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

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

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

Consider your summer job… Suppose you make $10/h HoursPay P – 0 = – 10 = – 20 = – 30 = 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…..

Consider y = x XY Y Y The second difference is constant, so it must be a polynomial of degree 2!

Try y = x 3 + 1

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.

What type of polynomial?

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