Math Help

• 800mans wrote on 2013-03-01 07:31
  Say I was determining a relationship between two variables.
  I predicted it to model somewhat of the equation y=x^2
  My excel equation is y= 0.a x^2 -bx -c
  
  
  I'm currently in high school so I haven't learned any statistics at all. Is there a way to analyze this?
  
  For example can I assume that -bx is directly proportional to x by some constant b, etc.
• December wrote on 2013-03-01 10:14
  I'm a little confused about what you're trying to do, but I assume you're trying to find the equation of a parabola given a picture of the graph.
  
  Start off with:
  

  [SIZE="3"]Y = Ax^2 + bx + c[/SIZE]

  
  
  Which you can convert to turning point form via method of Completing the square:
  

  [SIZE="3"]y = a(x + b/2a)^2 + c - (b^2)/4a[/SIZE]

  
  
  Then obverve your graph's turning point to get the co-ordinates of the turning point. eg (Xtp , Ytp) = (5, -3)
  Which you can equate to your turning point form expression:
  Xtp = -b/2a
  Ytp = c - b^2/2a
  
  Rearranging your expression you can get b and c in terms of a:
  b = -2a*Xtp
  c = Ytp + 2a(Xtp)^2
  
  Sub those two expressions back into "y = a(x + b/2a)^2 + c - (b^2)/4" to get the relationship between Y and X in terms of "a"
  
  Then, pick any coordinate on your graph (pick something with an easy number like 0 or 1 if possible) and sub those ordinates into X and Y of the above equation. Then it's possible to simplify the expression and find out that "a = ?????" (some number)
  
  Sub the answer into
  "b = -2a*Xtp
  c = Ytp + 2a(Xtp)^2"
  to obtain the values of B and C.
  
  Finally, you should have found the values for A, B and C.
  
  Hopely that helped.
• 800mans wrote on 2013-03-02 02:23
  Ohh srry about never I never gave details. I used a trendline in Excel which roughly gives you an equation that models a particular data points.
  I collected data from a lab and I expected the data to produce a 2nd degree exponential curve.
  But, I got something like 0.1300x^2+6.7x-3.73. I thought it would be y=x^2. How do I analyze why theres a 6.7x?
• December wrote on 2013-03-02 03:13
  y = x^2 is a quadratic aka second degree polynomial.
  y = 0.1300x^2+6.7x-3.73 is also a second degree polynomial but has gone under a series of dialations and translations. In otherwords, the reason why there is an 6.7x is because the graph has been shifted horitontally.
  
  My maths is a little rusty, but I tried rearranging that equation excel gave you into turning point form.
  y = 0.1300x^2+6.7x-3.73 is equivalent to y = 1300(x + 335/13)^2 - 11707400/13
  (Don't be afraid of the big numbers, it happens because we started with decimal numbers)
  
  So to go from y = x to y = 1300(x + 335/13)^2 - 11707400/13
  

  
  
  1. Dialation factor of 1300 from Y-axis ( the graph gets steeper)
     
  2. Tranlation 335/13 in the negative direction parallel to X-axis (the graph is moved roughly 25.77 units to the left)
     
  3. Translation 11707400/13 in negative direction parallel to Y-axis ( the graph is moved roughly 900,569 units down)