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How do you model functions to fit given conditions?

  1. Mar 9, 2007 #1
    for example, i want to find the coeffiecients of a function f(x) = ax^2 + bx + c for these given conditions:
    f(-1) = 3
    f(1) = 3

    i tried plugging and chugging
    for the first condition:
    3 = a - b + c
    3 = a + b + c

    now i tried subtracting the system to get
    0 = 2b
    so its solved that b = 0

    so now we got a step further towards the goal, and we know we can right the function as
    f(x) = ax^2 + c
    so now we try plugging and chugging again, but then we get
    3 = a + c
    3 = a + c
    since they are the same equation, i dont know how we can solve for a and c.
     
  2. jcsd
  3. Mar 10, 2007 #2

    Gib Z

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    Homework Helper

    lol you got the equation down to ax^2+c yes? Well for -1 and 1, x^2 is 1!

    So now you have it down to a+c=3! No need to solve for, choose any values :D
    1 and 2, 3 and 0, -4 and 7, whatever you want :D
     
  4. Mar 10, 2007 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You have an obvious problem here- your quadratic, f(x)= ax2+ bx+ c, has three coefficients and you only have two conditions. Given three points, not on a straight line, there exist a unique quadratic passing through them- but there are an infinite number of parabolas passing through two given points.

    Yes, as I said, you don't have enough conditions. You can solve for c in terms of a: c= 3- a. All of the parabolas given by f(x)= ax2+ 3- a will pass through (1, 3) and (-1, 3).
     
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