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Intro to Polynomial Functions

Intro to Polynomial Functions

Assessment

Presentation

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Medium

•
CCSS
HSF-IF.C.7A

Standards-aligned

Created by

Elizabeth Richardson

Used 27+ times

FREE Resource

12 Slides • 20 Questions

1

Intro to Polynomial Functions

Slide image

2

Multiple Choice

Which of the following expressions is in STANDARD FORM?

1

x3+ 5x −2x2+8x^3+\ 5x\ -2x^2+8

2

6x5+3x2−2x+16x^5+3x^2-2x+1

3

5+2x+3x25+2x+3x^2

3

STANDARD FORM

  • term with the largest exponent goes first

  • exponents decrease in order

4

Multiple Choice

Which expression is in STANDARD FORM?

1

−3x3+x2+5-3x^3+x^2+5

2

5+2x−3x25+2x-3x^2

3

4x4+3x−2x2−84x^4+3x-2x^2-8

5

Multiple Choice

What is the DEGREE of the expression

 4x3+2x5−8x+14x^3+2x^5-8x+1  

1

3

2

5

3

1

4

0

6

Multiple Choice

What is the degree of

 12x−5x2+x312x-5x^2+x^3  

1

1

2

2

3

3

4

12

7

Multiple Choice

What is the degree of

 2x6−12x5+x2−3x2x^6-12x^5+x^2-3x  

1

1

2

2

3

5

4

6

8

The DEGREE of a Polynomial is the HIGHEST EXPONENT

  • must be written out in standard form

  • no parenthesis

  • the LEADING COEFFICIENT will always be in front of the variable with the highest exponent

9

Multiple Choice

What is the degree of

 4−3x7−12x2+5x4-3x^7-12x^2+5x  

1

7

2

2

3

1

4

12

10

Multiple Choice

What is the degree of

 2x3(x+1)(x2−2)2x^3\left(x+1\right)\left(x^2-2\right)  

1

6

2

5

3

3

4

2

11

Remember there are no ( ) in standard form

Just add all the exponents

Don't forget x is the same as x1

~~ the one is included in adding the exponents

~~ the coefficients do not affect the degree

12

Multiple Choice

What is the degree of

 123x(76x3+1)(99x5−2)123x\left(76x^3+1\right)\left(99x^5-2\right)  

1

3

2

5

3

8

4

9

13

Multiple Choice

What is the LEADING COEFFICIENT OF

 3x4+8x2−10x+13x^4+8x^2-10x+1  

1

3

2

8

3

-10

4

1

14

Multiple Choice

What is the leading coefficient of

 4+8x−2x34+8x-2x^3  

1

4

2

8

3

-2

4

3

15

Multiple Choice

What is the leading coefficient of

 x4+25x3−8x+9x^4+25x^3-8x+9  

1

1

2

25

3

0

4

-8

5

9

16

Multiple Choice

Question image

This is the graph of

 y=x2 +8x −5y=x^{2\ }+8x\ -5  What's the degree and how many roots?

1

2; 2

2

8; 2

3

-5; 2

17

Multiple Choice

Question image

This is the graph of

 y=x3−4x+1y=x^3-4x+1  What's the degree and how many roots?

1

3; 3

2

-4; 3

3

1; 3

18

Multiple Choice

Question image

This is the graph of y=2x4+3x3-x2-x What is the degree and how many roots?

1

4; 4

2

3; 4

3

1; 4

19

Catching on to the Pattern???

  • The degree tells you how many ROOTS

  • Fundamental Theorem of Algebra

  • memorize this!!!!!!

20

You might have noticed one more thing...

  • Let's go back and check out the number of turns

  • How do they relate to the degree??

21

Multiple Choice

Question image

2nd degree Polynomial has ____ turns

1

0

2

1

3

2

4

3

22

Multiple Choice

Question image

3rd degree polynomial has ____ turns

1

0

2

1

3

2

4

3

23

Multiple Choice

Question image

4th degree polynomial has ____ turns

1

0

2

1

3

2

4

3

5

4

24

Multiple Choice

An 8th degree polynomial with have ___ roots and ____ turns

1

8; 7

2

8; 8

3

7; 8

4

9;8

25

ALMOST THERE....

  • Let's take a look at END BEHAVIOR

  • The degree and the leading coefficient will play a big role

26

This shows EVEN degree functions with a leading coefficient of +2 What do you notice about the ends?

Slide image

27

This shows EVEN degree functions with a leading coefficient of -2 What do you notice about the ends?

Slide image

28

This shows ODD degree functions with a leading coefficient of +2 What do you notice about the ends?

Slide image

29

This shows ODD degree functions with a leading coefficient of -2 What do you notice about the ends?

Slide image

30

Multiple Choice

Question image

Give it a try... What's the degree and the leading coefficient?

1

degree is odd; LC is +

2

degree is odd; LC is -

3

degree is even; LC is +

4

degree is even; LC is +

31

Multiple Choice

Question image

Give it another try... What is the degree and LC?

1

degree is odd; LC is +

2

degree is odd; LC is -

3

degree is even; LC is +

4

degree is even; LC is -

32

And that is our Intro to Polynomial Functions

Get ready to sum all this up in your notes and demo your understanding!

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Intro to Polynomial Functions

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