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ET: 2.2a (Copy)

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ET: 2.2a (Copy). Notes about graphs of polynomials Graph is continuous (Don’t have to pick up your pencil to draw it.) Graph is smooth Domain is all real numbers. Notes about equations of polynomials A n , a n-1 , a n-2 are real numbers N must be a nonnegative integer (whole #)

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slide1

ET: 2.2a (Copy)

Notes about graphs of polynomials

Graph is continuous (Don’t have to pick up your pencil to draw it.)

Graph is smooth

Domain is all real numbers

Notes about equations of polynomials

An, an-1, an-2 are real numbers

N must be a nonnegative integer (whole #)

Degree of the polynomial is the highest value of n.

  • Look at page 139
  • The graphs on the left are polynomials
  • The graphs on the right are not polynomials
slide2

More Parent Graphs

f(x) = x4, x6, x8, …xeven}

look like x2

f(x) = x5, x7, x9, …xodd}

look like x3

find the zeros make a quick graph
Find the zeros – Make a quick graph.

Even Multiplicity: Touch x-axis

Odd Multiplicity: Cross x-axis

Act like y = +1x3

Leading Coefficient/ Parent Function

slide6

Find the zeros – Make a quick graph.

At most how many zeros does f(x) have?

x = 0 x = 3

4

f(x) is degree 4.

Odd Multiplicity: Cross x-axis

What function will f(x) resemble?

y = -x4

parent function / leading coefficient

slide8

Roots of a 2nd degree polynomial are 2 and 3. Write a polynomial function that has the given zeros.

f(x) = (x – 2)( x – 3)

f(x) = -(x – 2)( x – 3)

f(x) = 7(x – 2)( x – 3)

Roots of a 3nd degree polynomial are 1 and -4. Write a polynomial function that has the given zeros.

f(x) = (x – 1)( x + 4)2

f(x) = (x – 1)2( x + 4)

f(x) = 3(x – 1)( x + 4)2

5 is the only root of a 7th degree polynomial write a polynomial function that has the given zero
5 is the only root of a 7th degree polynomial . Write a polynomial function that has the given zero.

f(x) = (x – 5)7

f(x) = 4(x – 5)7

f(x) = -(x – 5)7

Roots of a 2nd degree polynomial are 1 and .Write a polynomial function that has the given zeros.

f(x) = (x – 1)(x - )

assignment 2 2
Assignment 2.2

(Two Days: One Assignment worth double)

13-23 odd, 27-35, 41, 51, 56-57, 62, 66, 78, 79, 90, 97ab

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