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Given a quadratic satisfy the conditions of the limit

  1. Jul 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine values of a, b, c in the formula ax^2+bx^2 +c that satisfy the conditions:
    f(0)=0 // Limx->-1 F(x)=3 // limx->2 f(x)=6


    3. The attempt at a solution

    1.
    F(0)=0 therefore x=0

    so f(0)=a(0)^2+b(0)+c
    so f(0)=c = 0
    so c=0

    2.
    Lim f(x) = 3, x->-1

    so f(x)=ax^2+bx+c
    3 = a(-1)^2+(-b) + 0
    so a= 3+b or b= a-3

    3.
    f(x)=6 x->2

    6 = ax^2 + bx + c
    6 = 4a + 2b
    sub in a.
    6=4(3+b) +2b
    -6 = 6b
    b=-1

    now do the same but sub in b. to solve for a
    6=4a+2b
    6=4a + 2(a-3)
    6=4a + 2a -6
    12=6a
    a=2

    So therefore values are a=2, b=-1 and c=0 to satisfy those conditons.

    I beleive this is the correct way to go about it, but i just wanted some one to check for me if possible, and also i was curious is it because you are expressing a in terms of be and b in terms of a when taking the limit, and substituting that value into the next limit restriction 6=4a+2b that it makes it follow all of the previous conditions... (ie: c=0, b=a-3 a=3+b)

    I was just curious if some one could give me some more understanding if this is correct.
     
  2. jcsd
  3. Jul 17, 2012 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Your solution is correct, but after getting b=-1, you get a=3+b=2 directly.


    ehild
     
  4. Jul 17, 2012 #3
    thank you sir.
     
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