Assignment 18 (2A.3.1) Describing End Behavior and Turns Homework: Pgs.63-64 (1-10) & Read Pgs.65-68

Warm Up Workbook Warm-Up 2A.3.1

Notes Even-degree polynomial = largest exponent is even Odd-degree polynomial = largest exponent is odd Relative (or Local) Maximum = the turning point where the graph changes from increasing to decreasing; top of a hill. Relative (or Local) Minimum = the turning point where the graph changes from decreasing to increasing; bottom of a bowl. Roots/ zeroes/ x-intercepts = values which make the polynomial zero; where the graph crosses the x-axis. Nspire Exploration: Graph, compare, look for similarities (patterns) a. 𝑓 𝑥 = 𝑥! + 5𝑥! − 3𝑥! − 7𝑥 + 3 b. 𝑓 𝑥 = 𝑥! − 3𝑥! + 𝑥! − 7𝑥 + 3

c. 𝑓 𝑥 = 𝑥! − 7𝑥 + 6

d. 𝑓 𝑥 = 𝑥! + 𝑥! − 10 II. Change the leading term to negative III. Change the leading exponent to an odd number IV. Change the leading term to negative

End Behavior of Polynomials                        

 The maximum number of turning points is one less than the degree. Nspire Exploration #2: Roots 𝑓 𝑥 = 𝑥(𝑥 + 5)(𝑥 + 2)(𝑥 − 3)(𝑥 − 1) II. Take out a root III. Add some roots IV. Add an exponent to some roots Fundamental Theorem of Algebra A polynomial of degree “n” has “n” complex roots (they can be real or imaginary) Workbook Practice 2A.3.1 (1-10)

Polynomial End Behavior 𝑥!, 𝑥!,−𝑥!,−𝑥!, 𝑥!,−𝑥!, 𝑥!,−𝑥! 𝑥!, 𝑥!,−𝑥!,−𝑥!, 𝑥!,−𝑥!, 𝑥!,−𝑥!

𝑥!,−𝑥!, 𝑥!,−𝑥!, 𝑥!,… . 𝑥!…. 𝑥!,−𝑥!, 𝑥!,−𝑥!,−𝑥!  … .−𝑥!…. (Freestyle) 𝑥!, 𝑥!,−𝑥!,−𝑥!, 𝑥!,−𝑥!, 𝑥!,−𝑥!