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Quaratic Equations

  1. Jul 9, 2008 #1
    1. The problem statement, all variables and given/known data

    [tex] |ax^{2}+bx+c|\leq1 \forall x\in[0,1][/tex]
    Find the maximum magnitude of a,b, and c possible!

    My attempt:
    putting x=0;
    hence its maximummagnitude is 1.
    Help me with a and b.
  2. jcsd
  3. Jul 9, 2008 #2


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    Homework Helper

    You aren't going to be able to set limits on the coefficients separately, I think. You are probably going to have relationships between the coefficients.

    Picture it this way. The inequality is saying that

    -1 \leq ax^{2}+bx+c \leq 1[/tex] for [tex] 0 \leq x \leq 1[/tex].

    So a portion of the curve for this function has to fit entirely in the "box" bounded by x = 0, x = 1, y = -1, and y = 1. (Obviously, the parabola goes on forever elsewhere...) What does that mean for intersection points of the parabola with the "box"? How might you find coefficients from that?
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