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look at the given polynomial f(x)
whats the degree of f(x) ?

Ahh, actually im asking you a question to see if you know how to find the "degree"

oh!! i thought would be the exponent

yes, whats the degree of f(x) ?

i mean the degree is the exponent*

exponent of what

but then again I'm thinking its just 1

x^2?

ok...

what does finding the degree do for me though?

wow... ok

ok yes!! i see that now.

ok so finding the degree will give me the power function..

good, lets find the x intercepts

but now I'm not seeing how that would work.

thats right!
to find x intercepts, you want to solve \[\large -x^2(x-1)(x+3)=0\]

is this problem similar to the problem f(x)={3+x If x<0 // x^2 if x> not equal to 0....

use zero product property to get :
\(-x^2=0\) or \(x-1= 0\) or \(x+3=0\)

that gives you x intercepts : \(0, 1, -3\)

awesome!! ok so thats what i was thinking..

then id have to find the y intercept?

yes, simply put \(x=0\) in f(x) to get the y intercepts

f(x)=-x^2(x-1)(x+3)
f(0) = ?

-3

wouldn't i substitue all x values with 0?

yes, but -3 is wrong

f(x)=-x^2(x-1)(x+3)
f(0) = -0^2(0-1)(0+3)
= ?

+3

no, try again

what do you get when u multiply something by 0 ?

so..

so the answer is 0

haha happens :)

so the y intercept is 0

plot the points and read the graph and how it falls

look at the graph
https://www.desmos.com/calculator/bdlowvla6f

notice that the graph is crossing x axis at x=-3 and x=1
but it is just touching x axis at x=0

ok so it touches the x axis at 0,1,-3 but only crosses at 1 and -3

ooh you answered before i could finish typing.. but that is what i saw

very good!

the graph goes forever on both ends, it sinks down :
|dw:1440390580159:dw|

zoomout in that desmos link and see...

but what about the part that is between (0,0) and (1,0)?

what about it ?

|dw:1440390931586:dw|

if you see, the graph is just touching the x axis at x=0,
it is NOT crossing the x axis

the turning points happen where the function has 0 slope

|dw:1441149899004:dw|

you put a point where u calculating the turning point for example(0,0) is a turning point

|dw:1441150082317:dw|

is there a way to send you what I've written down and graphed?

take a picture and attach file on here

or click on draw and roughly draw what u have