1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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

    F(0)=0 therefore x=0

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

    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

    f(x)=6 x->2

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

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

    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


    User Avatar
    Homework Helper

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

  4. Jul 17, 2012 #3
    thank you sir.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook