I am trying to learn how different functions behave.
Arithmetic growth is when you add a constant to the previous value and its graph is a straight line. So, $y=2x$, for example, gives $y$ values: $2,4,6,8$, etc. where each successive $y$ value is found by adding $2$ to the previous $y$ value.
Exponential growth is different in that each successive $y$ value is found by MULTIPLYING the previous $y$ value by a constant. Example is $y=2^x$ ($2$ raised to the $x$ power).
Question: Given the way arithmetic and exponential growth behave, how can we describe quadratic growth (i.e. $y=x^2$). To me, this seems somewhere in the middle of arithmetic growth—adding a constant value to each successive $y$ value AND geometric growth, —-multiplying a constant value to each successive $y$ value, but I don't know exactly how to describe it.
Thanks for any help.