Mad_Math

     In general, a quadratic function will have the form of  f(x) = ax ² + bx + c ,    where a, b and c are constants and a  ≠ 0.    Do remember that in order to perform the method of completing the square, the coefficient of the  x ²  term in the quadratic expression  MUST  be equal to 1.      In this case, we are going to prove  where k is also a non-zero arbitrary constant.     To prove and thoroughly understand how the method of completing the square works on a quadratic function, we can actually visualize it by using paper-folding technic. In order to do so, the materials that are required include an A4 sized paper, a pen, a cellophane tape and a pair of scissors or a paper cutting blade.      The procedures needed are as shown as follow. All the figures shown in the procedures are the top view of the A4 sized paper.     1.  Fold the A4 sized paper as shown in the figure below according to the sequence indicated.    2. Unfold the A4 sized paper and l abel the length of each side o