Sec 3.1 Polynomials and Their Graphs (std MA 6.0)

Objectives:•To determine left and right end behavior of a polynomial.•To find the zeros of a polynomial by factoring.

Determining left and right end behavior of a polynomial.

To determine the left and right end behavior of a polynomial we need to look at two things. 1.The leading coefficient of the function. 2.The degree of the function.

Recall xn and –xn.

We can summarize our findings in a table.

y = xn where n is even

y = -xn where n is even

y = xn where n is odd

y = -xn where n is odd

Ex 1. For the following graphs determine the left and right behavior of the graph.

a) y = 3x2+4x-6

b) y = -3x3+5x-8

c) y = x5-4x3+5

d) y = -2x4 + x3-2x2+6x-18

e) y =(x-2)(x+1)(x+2)

Zeros of a Polynomial FunctionIf P is a polynomial and c is a real number,

then the following are true.1.c is a zero of P.2.x = c is a solution of the equation P(x) = 0.3.x – c is a factor of P(x).4.x = c is an x-intercept of the graph of P.

Ex 1. Find the zeros of P(x) = x2 + x – 6 by factoring.

Ex 2. Find the zeros by factoring.a) P(x) = x3 – 3x2 – 10x

b) P(x) = x4 + x3 – 8x - 8

Ex 3. Find the zeros and determine the end behavior of each graph.

43( ) 3 7P x x x x a)

b) 2 3( ) 1 2 5P x x x x

c) 3 2( ) 2 4 8P x x x x

Class Work

Find the zeros and determine the end behavior.1. P(x)= -2x(x – 6)

2. P(x) = 9x2 + 18x -7

3. P(x)= (x-3)(x+4)(x-8)(x+7)

4. P(x) = 2x3 - 4x2 – 16x

HW #1 p262 1-3(describe the transformations) 5-10 all, 11-35 odd (find zeros and find end behavior)