Question

Pre-cal 12 Question!

Determine the equation in factored form for the polynomial graph.

I need the value of 'a' as well.

Ex. f(x)= ax^3 +x^2 + x +4

Please wait for the attachment.

Answer 1

Look at the given graph, what are the x intercepts ?

Answer 2

Well, I know that

x-int are -->
x=-2 multiplicity of 1
x=1 multiplicity of 2
x=3 multiplicity of 1

Answer 3

Excellent!
next use factor theorem to write an expression for the polynomial

Answer 4

if \(x=a\) is a zero, then \((x-a)\) is a factor of the polynomial

Answer 5

Yes, until now, this is what I think it is

p(x)= (x+2)(x-1)(x-3)
we need y-int and value of a

Answer 6

sorry (x-1)^2

Answer 7

use the information about multiplicity too

Answer 8

looks good !

Answer 9

p(x)= a(x+2)(x-1)^2(x-3)

Answer 10

lets see if we can find the value of \(a\)

Answer 11

ok

Answer 12

all we're given is a graph
so stare at the graph and see if we could use something. .

Answer 13

y-int?

Answer 14

yeah give it a try

Answer 15

ok wait a moment

Answer 16

it seems y intercept is -3 ?

Answer 17

yeah I think so

so, (0,-3)

Answer 18

plug that in and find \(a\)

Answer 19

so, this is what I think it is

p(x)=a(x-3)(x-1)^2(x+2)
-3= a(-3)(-1)^2(+2)
-3=-6a
so a= -3/-6= 0.5

Answer 20

looks good !

Answer 21

haha thank you very much for walking me through it. :)

Answer 22

np:)