SOLUTION: 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. a

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
--------------------------------------------------------
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
------------------------------------------------------
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".
================================================
Cheers,
Stan H.

RELATED QUESTIONS
Hello! I am unsure that this is the right topic to submit this question to, but I am... (answered by ankor@dixie-net.com)

Hi I am stumped on this problem as well. We have to have 2 equations and use the HES... (answered by KMST)

I have a problem I need to find the mean on this problem, and I know you add them up... (answered by jsmallt9)

ok well we are doing this in geometry but its a review from algebra P(2,5); 4x-y=8 We... (answered by jim_thompson5910)

I have no idea if this is the right topic, but oh well. Here is the problem I am doing or (answered by jim_thompson5910)

I am not certain what type of problem this is my daughter has so I hope I have selected... (answered by jim_thompson5910,MathTherapy)

how would you do this problem? I am stuck and cant remember well here is the problem 5x... (answered by richard1234)

My class is studying polynomials, trinomials, and rational expressions and I need help... (answered by shree840,miohmeye1)

I do not understand the problem at all. My teacher gave us the answers to check our work. (answered by stanbon)