Simple question, though I can’t get my head around the rearrangement necessary when solving this with a system of simultaneous equations.
Specifically, I need to join a quadratic to another function together at a set point where the join is perfectly smooth and continuous, i.e. the gradient is the same at those points. I also need the quadratic turning point to hit a y-value of exactly 55.
Function 1: $0.1e^{x-5}$
Function 2: Quadratic with conditions
The join happens when Function 1 hits a y-value of 2.
There are three points of information, and three unknowns in a quadratic, so I know it can be done.