1. 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.

2. 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 x n and –x n.

3. We can summarize our findings in a table. y = x n where n is even y = -x n where n is even y = x n where n is odd y = -x n where n is odd

4. Ex 1. For the following graphs determine the left and right behavior of the graph. a)y = 3x 2 +4x-6 b)y = -3x 3 +5x-8 c)y = x 5 -4x 3 +5 d)y = -2x 4 + x 3 -2x 2 +6x-18 e)y =(x-2)(x+1)(x+2)

5. Zeros of a Polynomial Function If 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.

6. Ex 1. Find the zeros of P(x) = x 2 + x – 6 by factoring.

7. Ex 2. Find the zeros by factoring. a)P(x) = x 3 – 3x 2 – 10x b) P(x) = x 4 + x 3 – 8x - 8

8. Ex 3. Find the zeros and determine the end behavior of each graph. a) b) c)

9. Class Work Find the zeros and determine the end behavior. 1. P(x)= -2x(x – 6) 2. P(x) = 9x 2 + 18x -7 3. P(x)= (x-3)(x+4)(x-8)(x+7) 4. P(x) = 2x 3 - 4x 2 – 16x

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