anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
you know this problem?
dumbcow
  • 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
  • anonymous
wait, a*x?

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dumbcow
  • dumbcow
sorry, just means multiplying
anonymous
  • anonymous
a*x?
anonymous
  • anonymous
where you get a and x anyway?
dumbcow
  • dumbcow
a is like a scale factor, it determines how skinny or wide the graph is kind of like the slope
anonymous
  • anonymous
so it should be x infrotn of (-1) etc?
dumbcow
  • dumbcow
no i was replacing x with -1 because the function passes through the point (-1,16) where the x_value is -1
anonymous
  • anonymous
then -1(-1) etc, ? i got confused with ax , but i get it the you replace it.
anonymous
  • anonymous
i understand what you have to do next, multy,
dumbcow
  • 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
  • dumbcow
yes multiply and get a by itself
anonymous
  • anonymous
yeah i see it, so is going to be , 16=-1(etc?
dumbcow
  • dumbcow
yeah
anonymous
  • anonymous
ok thx, going go to sleep, at what time you usually on dude?
dumbcow
  • dumbcow
depends, usually at night im on pacific time
anonymous
  • anonymous
ok, so at this time?
dumbcow
  • dumbcow
yeah and definitely later too
anonymous
  • anonymous
ok, bye
anonymous
  • anonymous
hey, ok, you subtitude, then what?
anonymous
  • anonymous
was stoke for awhile, while working on it
dumbcow
  • 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
  • anonymous
what i got right now 16=a(-1)(-1+3)(-1-1)
dumbcow
  • dumbcow
ok use PEMDAS do the parenthesis first (-1-1)^2 = (-2)^2 = 4
anonymous
  • anonymous
ok now you got, 16=a(-1)(4)
dumbcow
  • dumbcow
what happened to the (-1+3) ??
anonymous
  • anonymous
forogt..
anonymous
  • anonymous
8
dumbcow
  • dumbcow
yep good 16 = a(-1)(8)
anonymous
  • anonymous
16=-8a -2=a
anonymous
  • anonymous
we found a, now we must replace a with -2
dumbcow
  • dumbcow
correct now use that and put it back in the equation
anonymous
  • anonymous
to what equipon. 16=-2x(x+3)(x-1)^2?
dumbcow
  • dumbcow
the very first one now we put the x's and y's back in
anonymous
  • anonymous
?
dumbcow
  • dumbcow
f(x) = ax(x+3)(x-1)^2
dumbcow
  • dumbcow
just replace a with -2
anonymous
  • anonymous
-2a(1)(9) -18a
anonymous
  • anonymous
how you find the fourt root?
dumbcow
  • dumbcow
woah not x, replace a with -2 thats what we just solved for
dumbcow
  • dumbcow
??? fourth root of what
anonymous
  • anonymous
you looking for the fourt root
dumbcow
  • dumbcow
no its a fourth degree polynomial it just means our function has a x^4 term
anonymous
  • anonymous
ok, how you start then?
dumbcow
  • dumbcow
i dont know what you mean you just did it answer is f(x) = -2x(x+3)(x-1)^2
anonymous
  • anonymous
but the question is, find the fourt root
anonymous
  • anonymous
oh NOT
anonymous
  • anonymous
is find the fourt dree polynomial function
anonymous
  • anonymous
i thought all along,to find the fourt root
dumbcow
  • dumbcow
there are 3 real roots 0,-3,1
anonymous
  • anonymous
no really, their is four, 1 has multicplicity of 2
dumbcow
  • dumbcow
correct
anonymous
  • anonymous
ok thank, yoiu being great help to me,good night
dumbcow
  • dumbcow
:)

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