1. Increasing/Decreasing; Minimums/Maximums Unit 2 (2.2 Polynomial Functions)

2. Warm-Up Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

3. Objectives  Students will be able to find the minimums and maximums of a polynomial using the calculator  Students will be able to identify the intervals on which the graph of a polynomial is increasing and/or decreasing  Students will be able to graph a polynomial (using the LCT, zeros and mins/maxs) Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

4. Relative Maximum and Minimum Values Copyright © by Houghton Mifflin Company, Inc. All rights reserved. x y x y Relative minimum Relative maximum

5. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. – 6 6 6 Zoom In: – 0.86 – 4.79 – 1.79 2.14 Zoom In: 0.580.76 -3.24 -3.43 The approximate minimum is (0.67, –3.33).

6. Copyright © by Houghton Mifflin Company, Inc. All rights reserved.  Press:  2 nd Calc  3:minimum  Left Bound?  Right Bound?  Guess?  TI-84 TI-84 The exact value is (0.67, –3.33).

7. Practice Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

8. Increasing and Decreasing Copyright © by Houghton Mifflin Company, Inc. All rights reserved.  Increasing – When the graph is growing or going up  Decreasing – When the graph is falling or going down  **Always in terms of the x values!  Written in interval notation (x-values!)

9. The graph of y = f (x): Copyright © by Houghton Mifflin Company, Inc. All rights reserved.  Increases on _____________  Decreases on ______________  Increases on ______________ (3, – 4) x y (–3, 6) –2–2 2

10. Practice Problems Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

11. Working Backwards Copyright © by Houghton Mifflin Company, Inc. All rights reserved.  Write the equation of least degree with the following roots:  1. 3, 4, -2  2. -1, 7, 2i, -2i  3. 0 multiplicity 3, 4, 2 multiplicity 2.

12. Closure Copyright © by Houghton Mifflin Company, Inc. All rights reserved.

13. Classwork/Homework  Worksheet (Graphing Polynomials)  Review tomorrow  Quiz Monday!! (on Graphing Polynomials) Copyright © by Houghton Mifflin Company, Inc. All rights reserved.