When we talk about a straight line :
$$ y=mx+b $$
a line is parallel to another if their $m$ is the same (disregarding the $b$), is that right?
What happens when we talk about a curve such as:
$$ y=nx^2+mx+b $$
If we have two curves like this, how can we judge if they are parallel or approximately parallel?
EDIT:
I'm sorry for the rough drawing
but in the image you can see two red curves (let's say they are generated by polynomials of degree 2) and one green curve. I would like some judgment that let me know that the red curves are ( even approximately ) parallels while the green one is not.
Two curves are parallel if at any point you draw a line perpendicular to the tangent line and passes through the point of tangency (the normal line), the normal lines are all parallel, at any point along the curve, and the distance between the line's points of intersections with the two curves are all the same.
See here: Math Curve Parallel Curves