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# Sec 3.1 Polynomials and Their Graphs (std MA 6.0) - PowerPoint PPT Presentation

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.

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### 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.

To determine the left and right end behavior of a polynomial we need to look at two things.

The leading coefficient of the function.

The degree of the function.

Recall xn and –xn.

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

• y = 3x2+4x-6

• y = -3x3+5x-8

• y = x5-4x3+5

• y = -2x4 + x3-2x2+6x-18

• y =(x-2)(x+1)(x+2)

If P is a polynomial and c is a real number, then the following are true.

• c is a zero of P.

• x = c is a solution of the equation P(x) = 0.

• x – c is a factor of P(x).

• x = c is an x-intercept of the graph of P.

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

• P(x) = x3 – 3x2 – 10x

• b) P(x) = x4 + x3 – 8x - 8

Class Work graph.

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)