I'm designing a web service that finds the regression function of a pattern within an image.
I analyzed three images and found the following three regressions:
1) $f(x) = 74.7602 + 0.2005x - 0.00091891x^2$ (domain: 0 ≤ x ≤ 200)
2) $f(x) = 102.337 + 0.349x - 0.002x^2$ (domain: 0 ≤ x ≤ 200)
3) $f(x) = 103.417 + 0.074x + x^2$ (domain: -8 ≤ x ≤ 8)
When these functions are plotted on a graph, functions 1 and 2 are more similar in shape. Function 3 is very narrow and has an up-facing concave (whereas functions 1 and 2 have a down-facing concave). How can I compare these three functions and mathematically determine that the curves of functions 1 and 2 are more similar? I don't care where on the coordinate plane the curves are, I just want to know if the shape is the same.
I was thinking about the obvious: plugging in points and checking for similarity, however this will not work if the function has a different scale. Do you know how I should begin?
P.S. I'm currently taking precalculus, so if you could describe this on my level (if possible), it would be greatly appreciated!