Question 175772: Well I am pretty sure this is the topic we are doing. The one i selected above.
Well anyways, this is the problem I have just been stuck on for EVER. it has 3 part, A, B, and C. and you cant get B or C if you dont get A. and ive been stuck on A. but even if i get past A, Im stil not quite sure if i know what to do with B and C.
Let p(x)=x(x-3)^2(x+1)
A) Sketch this graph of p(x). Label all intercepts. <-- I'm not even sure i know how to graph this at all. could you walk me through it?
b)Find another polynomial funtcion, q(x), that has the same zeroes as p(x) and goes throught the point (-1,16). <--- once i get the first graph I'm not sure How i would MAKE it go through (-1,16), How would i go upon doing that?
c) Explain how to determine the end behavior of a polynomial function. <--- what does it mean by determine if we already solved it above?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Let p(x)=x(x-3)^2(x+1)
A) Sketch this graph of p(x). Label all intercepts. <--
x-intercepts: x = 0, x= 3 with multiplicity 2, x= -1
y-intercept: P(0) = 0(0-3)^2(0+1) = 0
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b)Find another polynomial funtcion, q(x), that has the same zeroes as p(x) and goes throught the point (-1,16). <--- once i get the first graph I'm not sure How i would MAKE it go through (-1,16), How would i go upon doing that?
Consider q(x) = x(x-3)^2(x+1)+16
This has the same zeroes as p(x)
and q(-1) = 16
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c) Explain how to determine the end behavior of a polynomial function. <--- what does it mean by determine if we already solved it above?
"end behavior" refers to the y-values as x gets increasingly large
Since the highest power term determines that y value look
at x(x-3)^2(x+1) = x^4+....
As x gets larger x^4 gets larger so y gets larger and the
end behavior is "y gets increasingly larger".
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Cheers,
Stan H.
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