Question

EMERGENCY! I REALLY NEED HELP ON THIS QUESTION! WILL MEDAL!

Answer 1

HERE IS THE QUESTION

Answer 2

@vera_ewing @Howard-Wolowitz @paki @ganeshie8 @just_one_last_goodbye @Calcmathlete @phi @tkhunny

Answer 3

@amistre64 please help!

Answer 4

whats the trouble?

Answer 5

I don't understand how to do it

Answer 6

I know I have to place the points in, but I dont know which parts go where to solve it

Answer 7

what part of it DO you understand ... what is a multiplicity?

Answer 8

a multiplicity is what you multiply by?

Answer 9

it goes in the front like y=muultiplicity _____

Answer 10

hmm, no, it simply means there is more than one of the parts that is affected

Answer 11

take (x+b)^2 and write it as: (x+b)(x+b)

y = a (x+b) (x+b) (x-c)

now when x=-1, only 2 of these parts zero out .... which 2 do you think they would be?

Answer 12

if x=-1, wouldn't the x terms cancel? and get turned to -1

Answer 13

if x=-1 then yes, the xs become -1

0 = a (-1+b) (-1+b) (-1-c)

we are told that only 2 parts of this zero out ... a multiplicity of 2 ... when x=-1

which parts would you say zero out?

Answer 14

Okay, then the b terms would zero out?

Answer 15

yes, there are 2 identical parts ... x+b .. it stands to reason that these zero out

-1+b = 0, what is the value of b?

Answer 16

b would be 1

Answer 17

good we have one variable solved for

y = a(x+1)^2 (x-c)

now, we can use the other point values, what are they?

Answer 18

(4,0) and (0, -12)

Answer 19

so, y=0 when x=4 is also a root lets use it

0 = a(4+1)^2 (4-c)

what can we determine from this? what is the value of c?

Answer 20

ummm c would be 4 and a would be 0

Answer 21

a is not 0, a is unknown at the moment ... c=4 zeros out so lets use that

y = a(x+1)^2 (x-4)

now we can use the last point, when x=0, y=-12


-12 = a(0+1)^2 (0-4)

now solve for a

Answer 22

if a was 0, then y would always be zero regardless of the value for x, since 0 times anything else is zero

Answer 23

okay a would be 3

Answer 24

a=3 is correct

Answer 25

so the asnwer is 3?