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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.

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  1. amistre64
    • 3 years ago
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    no cowering away from a challenge now ;)

  2. magepker728
    • 3 years ago
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    lol just by looking at it made me slap myself lol

  3. amistre64
    • 3 years ago
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    :)

  4. amistre64
    • 3 years ago
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    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
    • 3 years ago
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    well if you can explain how to do it, ill really appreciate it

  6. amistre64
    • 3 years ago
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    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
    • 3 years ago
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    since the first and last slopes are just multiples of each other, we can do this one with 4 equations

  8. magepker728
    • 3 years ago
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    wow never taught of it this way lol.. looks like i have another problem to copy and save in my folder lol

  9. amistre64
    • 3 years ago
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    i had never had the notion to even consider this until a post about it yesterday that i was on

  10. amistre64
    • 3 years ago
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    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
    • 3 years ago
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    replacing my known slopes with a b and c defined a general setup :) yay

  12. magepker728
    • 3 years ago
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    your amazing lol

  13. amistre64
    • 3 years ago
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    im curious if i introduce a derivative as a slope if i can get a section between verts to be a curve

  14. amistre64
    • 3 years ago
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    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
    • 3 years ago
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    i guess we can forgo the negative in front .... of my setups :)

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