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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.

Sec 3.1 Polynomials and Their Graphs (std MA 6.0)

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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.

### 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.

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)

### Zeros of a Polynomial Function

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 2. Find the zeros by factoring.

• P(x) = x3 – 3x2 – 10x

• b) P(x) = x4 + x3 – 8x - 8

a)

b)

c)

### 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