I was hoping to get some advice on the best way to handle this problem. When fitting a quadratic with 3 points, I use a matrix approach to evaluate the coefficients which works nicely. In this case, I have only 2 points but an extra condition. I tried to evaluate the coefficients by simultaneous equations but this was painfully slow and I did not get the right equation.
The conditions are:
My answer is:
Which satisfies the first 2 conditions but not the third. Any advice on the easiest way to go about this would be greatly appreciated.