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.

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Sec 3 1 polynomials and their graphs std ma 6 0

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
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
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
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 1 find the zeros of p x x 2 x 6 by factoring
Ex 1. Find the zeros of P(x) = x2 + x – 6 by factoring.


Ex 2 find the zeros by factoring
Ex 2. Find the zeros by factoring.

  • P(x) = x3 – 3x2 – 10x

  • b) P(x) = x4 + x3 – 8x - 8



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


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