XPost: sci.math, sci.math.symbolic   
   From: marsh@privacy.net   
      
   On Sun, 2 Jan 2005, Dr. Muhammad Masroor Ali wrote:   
      
   > I have four quadratic equations of the form,   
   > y = a x^2 + bx + c, where 0 <= x <= 1.   
   >   
   > I need to find the maximum and minimum values of y (from four values)   
   > for each point in the range of x ([0.0,1.0]). I know that I can plot   
   > the equations and find the result visually. But is there a way of   
   > solving this analytically?   
   >   
   The extreme values of y are at 2ax + b = 0   
      
   If -b/2a is outside of [0,1], then the extreme values are at 0 and 1.   
   Otherwise use -b/2a and check values at 0 and 1 for other extreme.   
      
      
   > The situation is further complicated by the fact that not a single   
   > equation gives the min (max) value in that range, the lines do   
   > intersect and the equation giving min (max) do change.   
   >   
   > Any suggestion will be highly appreciated.   
   >   
      
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