1. A LGEBRA 2 5.3 Day 1 Polynomial Functions

2. R ECALL

3. L EADING COEFFICIENT

4. E XAMPLE 1

5. R EAL WORLD – E XAMPLE 2 RESPIRATION The volume of air in the lungs during a 5-second respiratory cycle can be modeled by v ( t ) = –0.037 t 3 + 0.152 t 2 + 0.173 t, where v is the volume in liters and t is the time in seconds. This model is an example of a polynomial function. Find the volume of air in the lungs 1.5 seconds into the respiratory cycle.

6. E XAMPLE 3

7. Y OU TRY Find g (2 x + 1) – 2 g ( x ) if g ( b ) = b 2 + 3. A.1 B.2 x 2 + 4 x – 2 C.2 x 2 + 4 x + 10 D.2 x 2 – 2

8. E XIT S LIP

9. A LGEBRA 2 5.3 Day 2 Polynomial Functions

11. Zeros of Even- and Odd-Degree Functions Odd-degree functions will always have an odd number of real zeros. Even-degree functions will always have an even number of real zeros or no zeros at all. The number of turns is always one less than the degree.

12. E XAMPLE 1 For each graph, Describe the end behavior Determine whether it represents an odd-degree or an even-degree polynomial function State the number of real zeros a)b)

13. Y OU TRY For the graph, determine whether it represents an odd-degree or an even-degree function, and state the number of real zeros.

14. E XIT S LIP For the graph, Describe the end behavior Determine whether it represents an odd-degree or an even-degree polynomial function State the number of real zeros