1. The problem statement, all variables and given/known data The problem consists of investigating the area between two functions of the forms (Parabolic segment): : y = mx + c and y = ax^2 + bx + c The investigation involves finding a combination that has one of each of the above functions and finding an area of one. The area between the functions has to be in the first quarter (positive x and y). 2. The attempt at a solution My investigation up to now has found the following: Function 1: 6x^2 - 2x + 8 Function 2: 4x + 8 These give points of intersection of: (0,8) and (1,12). These are the lower and upper bounds when integrating. Integration produces: Curve: 3x^2 - x^2 + 8x [Boundaries of 0 and 1]: Area under curve = 9 (between 0 and 1). Line: 2x^2 + 8x [Boundaries of 0 and 1]; Area under line = 10 (Between 0 and 1). => Area between line and curve is: 10 - 9 = 1 3. Further investigations I have already found that the coefficient of A (Parabola) has to be a multiple of 3, otherwise there will be a recurring decimal when integrated. My next steps involve: : Producing any generalisations that affect finding this specific area with these two functions. : Proving/generalising using Algebra.