graphs of polynomialsjoannemusa.weebly.com/uploads/2/4/5/0/24509955/graphing_polyno… · iii....

AdvAlg4 Name_______________________________ Date________________________Pd_____

GRAPHSOFPOLYNOMIALS

I.ZEROS&MULTIPLICITY:Statethezerosofeachpolynomial,themultiplicityofeachzero,andstatewhetherthegraphwillcrossatthex-axisorbounceatthex-axis.

a) f(x)=(x–3)2(x+4) b) f(x)=x(x+5)(x–2) c) f(x)=x2(x-7)3(x+1)2II.FINDINGZEROSBYFACTORING:Findthezerosofeachpolynomialbyfactoring.Listthemultiplicityofeachzero.RemembertofactortheGCFfirst,thenseteveryfactorequaltozeroandsolvefor“x”.

a. 𝑥! − 2𝑥! − 15𝑥GCF:_________Zeros&Multiplicities:

b.4𝑥! + 8𝑥! − 12𝑥GCF:_________

Zeros&Multiplicities:

c.-2𝑥! + 10𝑥! + 12𝑥!GCF:_________

Zeros&Multiplicities:

d.3𝑥! + 18𝑥! + 27𝑥GCF:_________

Zeros&Multiplicities:

III.GRAPHINGPOLYNOMIALS.GraphthepolynomialsfromsectionII.Usethezeros,multiplicities,andendbehaviorpropertiestohelpsketchthegraphs.

a) b)

c) d)

IV.MOREPRACTICE.a)Withoutacalculator,sketchagraphofthefunctionf(x)=(x+2)2(x–2)(x–3).Identify:ZEROS_______________,DEGREE__________,LEADCOEFFICIENT_________,ENDBEHAVIOR________________,Y–INTERCEPT_______________

b)Withoutacalculator,sketchagraphofthefunctionf(x)=-2x2(x+4)(x–1)3

Identify:ZEROS_______________,DEGREE__________,LEADCOEFFICIENT_________,ENDBEHAVIOR________________,Y–INTERCEPT_______________

c) Findthezerosofthefunctions.Statethemultiplicityofallzeros.Sketchagraphofthefunctionusingkeyfeatures(zeros,y–intercept,endbehavior)andmultiplicityrules.

1.f(x)=𝑥(𝑥 − 8)! 2.f(x)= (2𝑥 + 5)(𝑥 − 3)!

3.f(x)=𝑥! − 8𝑥! + 16𝑥!