Topic #5 Polynomial Functions

Topic 5 ObjectivesAfter completing the topic Polynomial

functions, students will be able tounderstand the relationship between the degree

of a polynomial and the number of real zeros it has, as detailed in the Fundamental Theorem of Algebra and related theorems;

understand the relationship between the degree of a polynomial function and the number of local extreme values of the function;

describe the end behavior of polynomials of odd and even degree.

Topic 5 Vocabulary (due next Friday)periodic function, degree of a polynomial, absolute or global maximum or

minimum, local maximum or minimum, interval notation, long-term or end behavior, zeros of a function

Evaluate the following functionsFind f(-2) for each of the following function of

each function and describe the end behavior.

Ex1:

Ex2:

Ex3:

322)( 23 xxxf

11023)( 234 xxxxxf

DrillFind f(-1) and f(3) for each of the following

function of each function and describe the end behavior.

1.

2.

3. complete Activity Sheet #2, #8

322)( 23 xxxf

11023)( 234 xxxxxf

DrillFind f(-1) and f(2) for each of the following

function of each function and describe the end behavior.

1.

2.

12)( 3 xxxf

11022

1)( 24 xxxxf

DrillSolve each equation using the quadratic formula.

1.

2.

0102 2 xx

3124 22 xxx

DrillIdentify the equations of the following functions.

1. Quartic Function with zeros at -3, 0, 1, and 2

2. Sixth degree with 4 real zeros

3. Cubic polynomial withand a y-intercept of -6

4. Quadratic function with no real zeros

xasxf )(