Describe the graph of the function f(x) = x3 − 18x2 + 101x − 180. Include the y-intercept, x-intercepts, 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

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- jamiebookeater

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- welshfella

the y intercept occurs when x = 0
so what do you think the y-intercepts is?

- anonymous

how would I find the Y intercept?

- welshfella

plug in x = 0 and work it out

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- welshfella

0^3 - 18(0)^2 + 101(0) - 180 = ?

- anonymous

y=180?

- welshfella

-180

- anonymous

so x=0 and y=-180 how would I figure out the shape of the graph?

- welshfella

well 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

so far I got 180=x^3 - 18^2 + 101x

- welshfella

- 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

or we might be able to factor by grouping which would be a lot quicker:-
x3 − 18x2 + 101x − 180

- anonymous

I got 3 answers and I don't know which one is right
x = 9
x = 5
x = 4

- welshfella

nope cant do it that way

- welshfella

how did you get those?

- welshfella

- they might all be right. A cubic equation will have 3 roots.

- welshfella

f(5) = 5^3 - 18(25) + 101(5) - 180 = 0
yes 5 is a root

- anonymous

im so confused, so x would be 5 and y is -180

- welshfella

did you get a calculator or wolfram to do it?

- welshfella

no x = 5 when y = 0

- welshfella

how did you get those 3 roots They are all correct I just checked them on my calc.

- anonymous

I couldn't figure it out so I used a calculator

- welshfella

oh 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

to 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

so the shape is a loop?

- welshfella

|dw:1441220571153:dw|

- welshfella

either like that

- welshfella

or like this
|dw:1441220677250:dw|

- welshfella

f(3) = -12
so it will be the first one

- welshfella

|dw:1441220810360:dw|

- anonymous

wow thank you so much!

- welshfella

yw

- welshfella

guess you should include the y intercept
|dw:1441220974136:dw|

- welshfella

- in fact i need not have found f(3) because the y intercept was negative anyway

- welshfella

- it had to be the first shape not the second. - i'd forgotten about the y-intercept

Looking for something else?

Not the answer you are looking for? Search for more explanations.