©2018TheAlgebros,LLC

2.3SketchingPolynomials

Review: Give the end behavior (both left and right) and the degree of the following functions:

1. 6(#) = −(# − 2)+ 2. 9(#) = −#; − #+ 3. <(#) = −3#) + 1# − 7#0

4. =(>) = −3>? + 12>@ − 4> 5. 9(#) = 3(# + 5)?(# − 3) 6.

For each function, give the zeros their behavior (crosses or is tangent).

7. 9(#) = (# − 6)A(# − 3)0 8. /(#) = −2#) + 2# 9. 3(#) = #; − 6#0 + 9#)

Sketch the following functions without graphing technology.

10. B(#) = #(# − 5)0(# − 3)CC 11. 6(#) = 3#) − #+ − 12# + 4

Degree: Leading Coefficient: Degree: Leading Coefficient:

End Behavior: Zeros and Behavior: End Behavior: Zeros and Behavior:

Sketch: Sketch:

15. D(#) = 2(2# + 1)(# − 5)+ 16. E(#) = −2#) + 32#

Degree: Leading Coefficient: Degree: Leading Coefficient:

End Behavior: Zeros and Behavior: End Behavior: Zeros and Behavior:

Sketch: Sketch:

2.3 PRACTICE

Diz D S D 4LC 1 LC 1 LC 7

3 Fans no 3 8k 3 EI 8,43 IEFu no G

D S D 74 12 LC 3 X x

X yFG no

q x kg x X neg Fox x

X yG no

q x Ycq x Gan no

X 6 crosses Rexx 21 2 1 KK x3626 1914 1 131 371 3

x 3 tangent RH 21kt'K Kk x3 35X l crosses crosses x crosses11 1 crosses X 3 tangent

x4xl 4 1BB x41kt4 462161

114111 16 3 I

X 2

it

2 1 4 Lxt4

3 2 3 2

X 0

EggIccrossest

xxs

x s tangent

I lki s

©2018TheAlgebros,LLC

17. 6(#) = 2#3 − #2 − 50# + 25 18. E(#) = −2#+(# − 5)(# + 5) Degree: Leading Coefficient: Degree: Leading Coefficient:

End Behavior: Zeros and Behavior: End Behavior: Zeros and Behavior:

Sketch: Sketch:

2.3SketchingPolynomials

1. Give the zeros and their behavior of the following function: 2. Sketch: 6(#) = 5#) − 80#

/(G) = 3G)(G − 4)(G + 2)0

Work backwards to create a possible function that each graph could represent. Show how you get your answer.

3. 4.

EXIT TICKET: Keeping it real! Not all polynomials are ideal for sketching by hand. Factor6(#) = 4#0 + 20#+ + 16 and

explain why it may be better to build a table of values or use technology to create a sketch.

WRAP UP

Fix 2x 1 1 2 25 SEEzeros

X2 2x 1 25 yBELOW

3 2 4 2X oltangent

EIg.EE Ia.eiiiI hxx3 giBYxFi5 recross

Foxi

DG

F't s5 manias