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Flight of Bird, Cubic Function

  1. Oct 21, 2012 #1

    CR7

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    1. The problem statement, all variables and given/known data

    A bird dove under water and re-emerged with a fish. Following is the table which shows the bird's estimated flight:

    Time(s),Height(m)
    0, 7
    2, 10
    4, 5
    6, 0
    7, 0
    8, 3

    Find a cubic equation to model the data.

    2. The attempt at a solution

    y=a(x-6)(x-7)(x-k) a,k are both unknown variables

    5=a(4-6)(4-7)(4-k) Substituted any 2 points from the table above

    5=a(-2)(-3)(4-k)

    5=6a(4-k)

    Not sure how to solve because there are 2 unknowns. Am I on the right track?
     
  2. jcsd
  3. Oct 21, 2012 #2
    You really only substituted 1 point, defined by two values (t, h).

    Try substituting one more different point into the original, then you'll have two equations with two unknowns.
     
  4. Oct 21, 2012 #3

    LCKurtz

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    Homework Helper
    Gold Member

    @cr7: What level of math are you taking? Are you given that the points come from a cubic so a cubic through any 4 points will automatically fit the others? Or have you studied least squares fitting? Of course, if the points are exactly from a cubic, least squares fit will give it too.
     
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