find a fourt-dregree polynomial function passing through the point (-1,16) with roots of 0,1(multiplicity 2), and -3, i am studying for a quiz

- anonymous

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- anonymous

you know this problem?

- dumbcow

f(x) = a*x(x+3)(x-1)^2
solve for a using given point
16 = a*(-1)(-1+3)(-1-1)^2
solve for a

- anonymous

wait,
a*x?

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- dumbcow

sorry, just means multiplying

- anonymous

a*x?

- anonymous

where you get a and x anyway?

- dumbcow

a is like a scale factor, it determines how skinny or wide the graph is kind of like the slope

- anonymous

so it should be x infrotn of (-1) etc?

- dumbcow

no i was replacing x with -1 because the function passes through the point (-1,16) where the x_value is -1

- anonymous

then -1(-1) etc, ? i got confused with ax , but i get it the you replace it.

- anonymous

i understand what you have to do next, multy,

- dumbcow

ah ok lets say you have a parabola
y = (x-1)^2
it has one zero at x=1 right?
but what about
y = 5(x-1)^2
it also has one zero at x=1, however its a different function, its a narrower parabola
so given the zeroes we can put the function into factored form but we dont know how the graph looks thats where the a comes from. the point given allows us to solve for a thus giving us the entire function

- dumbcow

yes multiply and get a by itself

- anonymous

yeah i see it,
so is going to be ,
16=-1(etc?

- dumbcow

yeah

- anonymous

ok thx, going go to sleep, at what time you usually on dude?

- dumbcow

depends, usually at night im on pacific time

- anonymous

ok, so at this time?

- dumbcow

yeah and definitely later too

- anonymous

ok, bye

- anonymous

hey, ok, you subtitude, then what?

- anonymous

was stoke for awhile, while working on it

- dumbcow

oh ok same one
so you substituted the x,y values in from the point they gave you
then you solve for a, get it by itself

- anonymous

what i got right now
16=a(-1)(-1+3)(-1-1)

- dumbcow

ok use PEMDAS
do the parenthesis first
(-1-1)^2 = (-2)^2 = 4

- anonymous

ok now you got, 16=a(-1)(4)

- dumbcow

what happened to the (-1+3) ??

- anonymous

forogt..

- anonymous

8

- dumbcow

yep good
16 = a(-1)(8)

- anonymous

16=-8a
-2=a

- anonymous

we found a, now we must replace a with -2

- dumbcow

correct
now use that and put it back in the equation

- anonymous

to what equipon. 16=-2x(x+3)(x-1)^2?

- dumbcow

the very first one
now we put the x's and y's back in

- anonymous

?

- dumbcow

f(x) = ax(x+3)(x-1)^2

- dumbcow

just replace a with -2

- anonymous

-2a(1)(9)
-18a

- anonymous

how you find the fourt root?

- dumbcow

woah
not x, replace a with -2
thats what we just solved for

- dumbcow

???
fourth root of what

- anonymous

you looking for the fourt root

- dumbcow

no its a fourth degree polynomial
it just means our function has a x^4 term

- anonymous

ok, how you start then?

- dumbcow

i dont know what you mean
you just did it
answer is
f(x) = -2x(x+3)(x-1)^2

- anonymous

but the question is, find the fourt root

- anonymous

oh NOT

- anonymous

is find the fourt dree polynomial function

- anonymous

i thought all along,to find the fourt root

- dumbcow

there are 3 real roots
0,-3,1

- anonymous

no really, their is four, 1 has multicplicity of 2

- dumbcow

correct

- anonymous

ok thank, yoiu being great help to me,good night

- dumbcow

:)

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