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Finding a parabolic equation with unknown variabilic constants?

  1. Aug 28, 2012 #1
    Hey folks,
    Bit of a complex question here, but I'm hoping someone smarter than myself can help me figure this out. I want to make a parabolic curve that is controlled by 2 constants S and T. I know that in y = Ax2 + Bx + C
    C = S
    as one of the points I can give from the if statements I'm working from gives the point (0,S)

    the other 2 point however make it difficult for me to convert 3 points to the equation as, well, you'll see:

    (T,100)
    (T+100,100)

    Can someone please help explain to me how to make these three points
    (0,S) (T,100) (T+100,100)
    into a parabolic equation without assuming a set value for either S or T
     
  2. jcsd
  3. Aug 29, 2012 #2
    Just a quick hint: the points (T,100) and (T+100,100) tell you that the parabola is symmetric about the line x=T+50, and so your equation has the form [itex]y=c+a(x-(T+50-b))(x+(T+50+b))[/itex] for some real numbers a, b and c.

    Edit: Here's maybe a better hint: the x-coordinate of the vertex of a parabola is at [itex]-b/2a[/itex], so that tells you, in this case, that [itex]-b/2a=150[/itex], and since you've already got c nailed down, you're just one equation away from specifying a unique parabola.
     
    Last edited: Aug 29, 2012
  4. Aug 29, 2012 #3
    Thank you for your help. even with your "better hint"(a=1 b=-300) I can't figure out how to make it parabolic, no matter what I do its a linear line. I can give you 3 example C|T's so you can tell what I mean, but I can't figure out how to get it to go through the 3 points (point 4 it must satisfy is (2T+100, S))
     
    Last edited: Aug 29, 2012
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