Do Now 3/6/2012

1. Do Now 3/6/2012 • Evaluate f(2) and f(-2): • f(x) = x3 – x2 – 4x + 4

2. Today’s Objective: • Graph polynomial functions and locate real zeros • Find the relative maxima and minima of polynomial functions

3. Vocabulary • Location Principle- • if f(a)< 0 and f(b) > 0, then there exists at least one zero between a and b • Relative maximum- a point on the graph of a function where no other nearby points have a greater y-coordinate • Relative minimum- a point on the graph of a function where no other nearby points have a lesser y-coordinate

4. Analyzing Graphs of polynomial functions • Graphing polynomial functions • Identify the end behavior • Create a table of values • Graph and connect points through smooth curves • Analyzing • Locate zeros of a Function • Identify maximum and minimum points • Explain turning points and make predictions

5. Graphing polynomial functions • Create a table of values • f(x) = x3 – 5x2 + 3x + 2 • Identify maximum number of zeros possible • Plug in x values to find f(x) • Extend table until you reach the maximum change in signs

6. Graph coordinates • Connect points with smooth curves • Remember this is a sketch it does not have to be perfect

7. Graph a Polynomial Function Graph f(x) = –x3 – 4x2 + 5 by making a table of values. Answer:

8. Do Now • What is a relative minimum and maximum?

9. Relative Minima and Maxima • In order to find: • Create an xy-table • Look at y values for increase and decrease in 3 consecutive values • If values increase and decrease between 3 consecutive numbers then there exist a relative maximum • If values decrease then increase there exist a relative minimum.

10. Analyzing Polynomial functions • Create a table of values • Identify number of zeros • Identify relative maximum and minimum points • Explain turning points and make predictions

11. Maximum and Minimum Points Graph f(x) = x3 – 4x2 + 5. Estimate the x-coordinates at which the relative maxima and minima occur. Make a table of values and graph the function.