Question

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

Answer 1

you know this problem?

Answer 2

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

Answer 3

wait,
a*x?

Answer 4

sorry, just means multiplying

Answer 5

a*x?

Answer 6

where you get a and x anyway?

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

i understand what you have to do next, multy,

Answer 12

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

Answer 13

yes multiply and get a by itself

Answer 14

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

Answer 15

yeah

Answer 16

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

Answer 17

depends, usually at night im on pacific time

Answer 18

ok, so at this time?

Answer 19

yeah and definitely later too

Answer 20

ok, bye

Answer 21

hey, ok, you subtitude, then what?

Answer 22

was stoke for awhile, while working on it

Answer 23

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

Answer 24

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

Answer 25

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

Answer 26

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

Answer 27

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

Answer 28

forogt..

Answer 29

8

Answer 30

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

Answer 31

16=-8a
-2=a

Answer 32

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

Answer 33

correct
now use that and put it back in the equation

Answer 34

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

Answer 35

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

Answer 36

?

Answer 37

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

Answer 38

just replace a with -2

Answer 39

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

Answer 40

how you find the fourt root?

Answer 41

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

Answer 42

???
fourth root of what

Answer 43

you looking for the fourt root

Answer 44

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

Answer 45

ok, how you start then?

Answer 46

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

Answer 47

but the question is, find the fourt root

Answer 48

oh NOT

Answer 49

is find the fourt dree polynomial function

Answer 50

i thought all along,to find the fourt root

Answer 51

there are 3 real roots
0,-3,1

Answer 52

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

Answer 53

correct

Answer 54

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

Answer 55

:)