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Determining increase/decrease intervals for ax^2+bx+c

  1. Nov 24, 2012 #1
    Hello,

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

    I am trying to determine on what intervals the parabola y=ax^2+bx+c increases/decreases, without resorting to differentiation.

    2. Relevant equations



    3. The attempt at a solution

    For the function to be increasing on a certain interval f(x1)>f(x2) for any x1 and x2 on that interval such that x1>x2. Hence, ax1^2+bx1+c>ax2^2+bx2+c. That yields, (x1+x2)>-b/a. How do I derive the expected x>-b/2a from that? That result could be obtained for x1=x2, hence Δ=0, but why is that and why ought it to be used in order to obtain the correct answer?
     
  2. jcsd
  3. Nov 24, 2012 #2

    mfb

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    Staff: Mentor

    Let x2=x1+Δ and then consider the limes of Δ->0?
     
  4. Nov 24, 2012 #3

    Dick

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    How about completing the square?
     
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