1. Analyzing Graphs of Polynomial Functions

2. With two other people: Each person pick a letter, f, g, or h Each person will graph their function After graphing each function, discuss the following questions with your partner: How many zeros does each graph have? How many turning points does each graph have? Is there a limit on the number of turning points a graph will have? The functions f(x) = 3 x⁵ - 2 x⁴ - 6 x³ + x² + 3 g(x) = 2 x⁵ - 3 h(x) = x⁵ + x⁴ - 4 x³ - 3 x² + 5 x

3. The graph of every polynomial function of degree n has at most n – 1 turning points If a polynomial function has n distinct real zeros, then its graph will have exactly n – 1 turning points

4. Local Maximum Highest point on a curve Local Minimum Lowest point on a curve EVERY turn or change of direction = local max/min Is it possible for a point to be a zero and a local max/min? HANDOUT

5. 1. f(x) = 2 x⁴ - 5 x³ - 4 x² - 6 X-intercepts ≈ -1.16 and 3.21 Local min ≈ (2.31, -32.03) and (-0.43, -6.27) Local max ≈ (0, -6)

6. P.377 # 29-34 all GRAPH & identify all x-intercepts and any local maximums or minimums. (round to the nearest hundredth when necessary)