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) PowerPoint PPT Presentation


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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)

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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.


We can summarize our findings in a table

We can summarize our findings in a table.


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


Ex 3 find the zeros and determine the end behavior of each graph

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

a)

b)

c)


Class work

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

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


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