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anonymous
 one year ago
Describe the graph of the function f(x) = x3 − 18x2 + 101x − 180. Include the yintercept, xintercepts, and the shape of the graph.
Can you give me then answer and tell me how you got it and walk me through it.
anonymous
 one year ago
Describe the graph of the function f(x) = x3 − 18x2 + 101x − 180. Include the yintercept, xintercepts, and the shape of the graph. Can you give me then answer and tell me how you got it and walk me through it.

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welshfella
 one year ago
Best ResponseYou've already chosen the best response.0the y intercept occurs when x = 0 so what do you think the yintercepts is?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how would I find the Y intercept?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0plug in x = 0 and work it out

welshfella
 one year ago
Best ResponseYou've already chosen the best response.00^3  18(0)^2 + 101(0)  180 = ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so x=0 and y=180 how would I figure out the shape of the graph?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0well try and find the x intercepts first they occur when y = 0 so we have the equation x^3 − 18x^2 + 101x − 180 = 0

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so far I got 180=x^3  18^2 + 101x

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0 solve for x by the rational roots theorem the roots could be factors 0f 180 like +/ 1, +/ 3, +/ 6 , +/5,+/ 6, +/ 9 so there's a lot to try out!

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0or we might be able to factor by grouping which would be a lot quicker: x3 − 18x2 + 101x − 180

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got 3 answers and I don't know which one is right x = 9 x = 5 x = 4

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0nope cant do it that way

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0how did you get those?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0 they might all be right. A cubic equation will have 3 roots.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0f(5) = 5^3  18(25) + 101(5)  180 = 0 yes 5 is a root

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0im so confused, so x would be 5 and y is 180

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0did you get a calculator or wolfram to do it?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0no x = 5 when y = 0

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0how did you get those 3 roots They are all correct I just checked them on my calc.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I couldn't figure it out so I used a calculator

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0oh i see well another way is to to try ouy values such as 3, 5 etc and once you have found one  say 5 you divide the function by x  5 using long or synthetic division to get a quadratic which you solve to get the other 2.

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0to find the shape you can differentiate and find slopes at different values of x We know it is probably a double loop because there are 3 rational roots.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the shape is a loop?

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441220571153:dw

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0or like this dw:1441220677250:dw

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0f(3) = 12 so it will be the first one

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0dw:1441220810360:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0wow thank you so much!

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0guess you should include the y intercept dw:1441220974136:dw

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0 in fact i need not have found f(3) because the y intercept was negative anyway

welshfella
 one year ago
Best ResponseYou've already chosen the best response.0 it had to be the first shape not the second.  i'd forgotten about the yintercept
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