1. Polynomial Behavior patterns in the graphs

2. Warm Up List and name the transformations in this diagram

3. Standard Form of Polynomial

4. DegreeName using degree Polynomial example Number of terms Name using # terms 0 5 1 1X + 42 24x 2 1 34x 3 - 3x 2 + x3 42x 4 + 5x 2 2 5-x 5 +4x 2 +2x +14

5. Lesson 4.4Graphing Polynomial Functions Key Terms: Relative Max / Min Real Zeros (x-intercepts) Example 1Graphing Polynomials A)B) Zeros: 1, -1.4, -3.6 R. Min: (-2.7, -4.5) R. Max: (0, 5)

6. Left & Right End Behavior Degree 0Degree 2Degree 3Degree 4Degree 1 Degree 2Degree 3Degree 4Degree 1 Negative Polynomials Positive Polynomials

7. Studying Graphs of Polynomials Odd Degree 1 Positive LC Even Degree 2 Positive LC Odd Degree 3 Positive LC Even Degree 4 Positive LC Odd Degree 5 Positive LC Odd Degree 5 Negative LC Even Degree 4 Negative LC Key Notes: [1] Odd when rt & lf ends go opposite directions [2] Even when rt & lf ends go in same direction [3] Positive right end goes up [4] Negative right end goes down [5] Degree is one more than the number of turns

8. Example 3Graphs of Polynomial Functions Determine if the polynomial is even/odd, Positive / Negative, find the Degree, and state the number of Real Zeros / Imaginary. a) Even Negative Degree 2 2 Real Zeros b) Odd Positive Degree 5 1 Real / 4 Imaginary Zeros

9. Determine if the polynomial is even/odd, positive/negative, and give the degree. c) d) Even Negative Degree 4 Odd Positive Degree 5

10. Power Functions are any function of the form f(x) = ax n where a and n are nonzero constant real numbers n is the exponent; 1.If If n = positive integer (linear, quadratic, cubic, etc) 2.If n = negative integer (rational function) 3.If n = fraction (square root function)

11. Power Functions are any function of the form f(x) = ax n If If n = positive integer (linear, quadratic, cubic, etc) f(x) = ax 3 f(x) = ax 4

12. Power Functions are any function of the form f(x) = ax n If n = negative integer (rational function) f(x) = ax -1 = 1/x

13. Power Functions are any function of the form f(x) = ax n 1.If n = fraction (square root function) f(x) = ax 1/2

14. Homework 4.4 1. a)b) Zeros: c) Rel. Max: Rel. Min: – 4, 0 (0, 0) (-2.7, -9.5)

15. Warm-Up [1] State the degree and LC: [2], find Degree 4 LC = 5

16. Example 2Polynomial Applications A)Suppose you have a 12 x 14 sheet of cardboard. You plan to cut a uniform corner from each corner and fold the sheet into an open box. - What is the maximum volume? - What are the dimensions of the maximized box? B)Use a 10 x 12 sheet of cardboard 10 – 2x 12 – 2xx Max V: 96. 8 units 3 Dimensions:1.8 x 6.4 x 8.4 160. 6 units 3 2.1 x 7.7 x 9.7