Question

This was fuunn!!!

Create an equation of absolute values with the given properties for the graph

slopes from left to right are: -4, -2, 1, 0, 4

you can define your own vertexes, but it has to match those slopes.

Answer 1

no cowering away from a challenge now ;)

Answer 2

lol just by looking at it made me slap myself lol

Answer 3

:)

Answer 4

with 5 slopes, we would need to setup up a system of 5 equations in 5 unknowns

i finally understood the dynamics to determine the slopes this morning

Answer 5

well if you can explain how to do it, ill really appreciate it

Answer 6

spose we name the parts for each slope as: a,b,c,d

we can construct the equations as such

-a-b-c-d = -4
-a-b-c+d = -2
-a-b+c+d = 1
-a+b+c+d=0

this gives us a solutions to:\[y=a|x-v_1|+b|x-v_2|+c|x-v_3|+d|x-v_4|\]

where the vs are the vertexes from left to right as well

Answer 7

since the first and last slopes are just multiples of each other, we can do this one with 4 equations

Answer 8

wow never taught of it this way lol.. looks like i have another problem to copy and save in my folder lol

Answer 9

i had never had the notion to even consider this until a post about it yesterday that i was on

Answer 10

i sat there this morning with my trusty little ti83; and wrote out an equation to test the dynamic with

y = 2|x-v1|+|x-v2|+2|x-v3|

and i found out that the corresponding graph had slopes between verts that matched up with:

-(2+1+2)
-(2+1-2)
-(2-1-2)
-(-2-1-2)

Answer 11

replacing my known slopes with a b and c defined a general setup :) yay

Answer 12

your amazing lol

Answer 13

im curious if i introduce a derivative as a slope if i can get a section between verts to be a curve

Answer 14

rref{{-1,-1,-1,-1,-4},{-1,-1,-1,1,-2},{-1,-1,1,1,1},{-1,1,1,1,0}}

the wolf gives me a matrix read out of the abcd so that

y = 2|x+2| -|x|/2+3|x-2|/2+|x-5| - 10 ; - 10 just to drop it down

hmm, but its reversed, right to left lol

http://www.wolframalpha.com/input/?i=y+%3D+2%7Cx%2B2%7C+-%7Cx%7C%2F2%2B3%7Cx-2%7C%2F2%2B%7Cx-5%7C+-+10

Answer 15

i guess we can forgo the negative in front .... of my setups :)