SOLUTION: How to set up a graph for this polynomial. I don't know where to start. Is there a way that I can know what the general shape of the graph will be before I start? I really need hel

Algebra ->  Graphs -> SOLUTION: How to set up a graph for this polynomial. I don't know where to start. Is there a way that I can know what the general shape of the graph will be before I start? I really need hel      Log On


   

Question 916232: How to set up a graph for this polynomial. I don't know where to start. Is there a way that I can know what the general shape of the graph will be before I start? I really need help
f(x) = (1/64)(x-3)^2(x+4)^3
Thank you
Found 3 solutions by stanbon, MathLover1, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How to set up a graph for this polynomial. I don't know where to start. Is there a way that I can know what the general shape of the graph will be before I start? I really need help
f(x) = (1/64)(x-3)^2(x+4)^3
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If x = 0, y = (1/64)(9)(64) = 9;; So, plot (0,9)
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Because (x-3) is squared, the graph touches but does not pass thru (3,0)
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Because (x+4) is raised to an odd poser, the graph passes thru (-4,0)
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Because the highest power is x^2*x^3 = x^5, the graph goes to -oo as
x goes to -oo and the graph goes to +oo as x goes to +oo.
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graph%28400%2C400%2C-10%2C10%2C-10%2C15%2C%281%2F64%29%28x-3%29%5E2%2A%28x%2B4%29%5E3%29
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Cheers,
Stan H.
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Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+%281%2F64%29%28x-3%29%5E2%28x%2B4%29%5E3+

x=0
f%280%29+=+%281%2F64%29%280-3%29%5E2%280%2B4%29%5E3+
f%280%29+=+%281%2F64%29%28-3%29%5E2%284%29%5E3+
f%280%29+=+%281%2F64%29%2A9%2A%2864%29+
f%280%29+=+%281%2Fcross%2864%29%29%2A9%2Across%2864%29+
f%280%29+=+9
point is (+0+,9)


x=-1
f%28-1%29+=+%281%2F64%29%28-1-3%29%5E2%28-1%2B4%29%5E3+
f%28-1%29+=+%281%2F64%29%28-4%29%5E2%283%29%5E3+
f%28-1%29+=+%281%2F64%29%2A%2816%29%2A27+
f%28-1%29+=+%281%2Fcross%2864%294%29%2Across%2816%29%2A27+
f%28-1%29+=+27%2F4
f%28-1%29+=+6.75
point is (+-1+,6.75)


x=1
f%281%29+=+%281%2F64%29%281-3%29%5E2%281%2B4%29%5E3+
f%281%29+=+%281%2F64%29%28-2%29%5E2%285%29%5E3+
f%281%29+=+%281%2F64%29%2A4%2A125+
f%281%29+=+%281%2Fcross%2864%2916%29%2Across%284%29%2A125+
f%281%29+=+7.8
point is (+1+,7.8)

x=-4
f%28-4%29+=+%281%2F64%29%28-4-3%29%5E2%28-4%2B4%29%5E3+
f%28-4%29+=+%281%2F64%29%28-7%29%5E2%280%29%5E3+
f%28-4%29+=+%281%2F64%29%2A%2849%29%2A0+
f%28-4%29+=+0
point is (+-4+,+0+)

x=4
f%284%29+=+%281%2F64%29%284-3%29%5E2%284%2B4%29%5E3+
f%284%29+=+%281%2F64%29%28-1%29%5E2%288%29%5E3+
f%284%29+=+%281%2F64%29%2A1%2A512+
f%284%29+=+512%2F64+
f%284%29+=+8
point is (+4+,+8+)

x=-5
f%28-5%29+=+%281%2F64%29%28-5-3%29%5E2%28-5%2B4%29%5E3+
f%28-5%29+=+%281%2F64%29%28-8%29%5E2%28-1%29%5E3+
f%28-5%29+=+%281%2F64%29%2A%2864%29%2A%28-1%29+
f%28-5%29+=+%281%2Fcross%2864%29%29%2Across%2864%29%2A%28-1%29+
f%28-5%29+=+-1

point is (+-5+,-1)

x=5
f%285%29+=+%281%2F64%29%285-3%29%5E2%285%2B4%29%5E3+
f%285%29+=+%281%2F64%29%282%29%5E2%289%29%5E3+
f%285%29+=+%281%2F64%29%2A%284%29%2A%28729%29+
f%285%29+=+%281%2Fcross%2864%2916%29%2Across%284%29%2A%28729%29+
f%285%29+=+729%2F16
f%285%29+=+45.6
point is (+5+,45.6)




so, we have points:
(+0+,9)
(+-1+,6.75)
(+1+,7.8)
(+-4+,+0+)
(+4+,+8+)
(+-5+,-1)
(+5+,45.6)






Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
dl the FREE graph software at
http://www.padowan.dk
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Use Ins and enter the function.