ALGEBRA 2 5 3 Day 1 Polynomial Functions

ALGEBRA 2 5. 3 Day 1 Polynomial Functions

RECALL

LEADING COEFFICIENT

EXAMPLE 1

REAL WORLD –EXAMPLE 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.

EXAMPLE 3

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

EXIT SLIP

ALGEBRA 2 5. 3 Day 2 Polynomial Functions

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.

EXAMPLE 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)

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

EXIT SLIP For the graph, Describe the end behavior Determine whether it represents an odd-degree or an evendegree polynomial function State the number of real zeros