ET: 2.2a (Copy)

1 / 10

# ET: 2.2a (Copy) - PowerPoint PPT Presentation

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 #)

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' ET: 2.2a (Copy)' - tom

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

ET: 2.2a (Copy)

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

Graph is smooth

Domain is all real numbers

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

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.

Even Multiplicity: Touch x-axis

Odd Multiplicity: Cross x-axis

Act like y = +1x3

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

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.

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

(Two Days: One Assignment worth double)

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