## amistre64 3 years ago 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.

1. amistre64

no cowering away from a challenge now ;)

2. magepker728

lol just by looking at it made me slap myself lol

3. amistre64

:)

4. amistre64

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

5. magepker728

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

6. amistre64

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

7. amistre64

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

8. magepker728

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

9. amistre64

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

10. amistre64

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)

11. amistre64

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

12. magepker728

13. amistre64

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

14. amistre64

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

15. amistre64

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