1. Classification of a Polynomial DegreeNameExample -2x 5 + 3x 4 – x 3 + 3x 2 – 2x + 6 n = 0 n = 1 n = 2 n = 3 n = 4 n = 5 constant 3 linear 5x + 4 quadratic 2x 2 + 3x - 2 cubic 5x 3 + 3x 2 – x + 9 quartic 3x 4 – 2x 3 + 8x 2 – 6x + 5 quintic

2. Warm-up Classify each polynomial by degree and by number of terms. a) 5x + 2x 3 – 2x 2 cubic trinomial b) x 5 – 4x 3 – x 5 + 3x 2 + 4x 3 quadratic monomial c) x 2 + 4 – 8x – 2x 3 d) 3x 3 + 2x – x 3 – 6x 5 cubic polynomial quintic trinomial e) 2x + 5x 7 7 th degree binomial Not a polynomial

3. Polynomial Graphs Short Quiz: Tomorrow 1/27/10 (maybe)

4. Polynomial Functions and Their Graphs There are several different elements to examine on the graphs of polynomial functions: Local minima and maxima:

5. On the graph above:A local maximum: f(x) = A local minimum: f(x) = Give the Local Maxima and Minima Must use y to describe High and Low

6. Finding a local max and/or local min is EASY with the calculator! Graph each of the following and find all local maxima or minima: Now describe their end behavior.

7. Describe the Interval of Increasing and Decreasing Increasing when ___________ Decreasing when _____________ Increasing when ___________ Must use x to describe Left to Right x y (Left to Right) The graph is:

8. Give the maximums and minimums and describe the intervals of increasing and decreasing, for each of the following:

9. Give the maximum and minimums and describe the intervals of increasing and decreasing, for each of the following:

10. Now, let’s do it on our own: For each of the following: sketch the graph find the points at which there is a local max or min describe the intervals in which the function is increasing or decreasing describe the end behavior

11. Now, let’s do it on our own: For each of the following: sketch the graph find the points at which there is a local max or min describe the intervals in which the function is increasing or decreasing describe the end behavior