If $y = Bx + c$, and B for x is the slope, how about in
$ y = B_{1} x^2 + B_{2} x + c$, what do you call the $B_{1}$?
I am trying to defined it in a paper and need to know what is the term called. I am defining something like
where c is the intercept, B_{1} is the slope and B_{2} is the...?
They represent finite differences. If
$f(x)=ax^2+bx+c$, then $f(0)=c$.
$g(x)=f(x+1)-f(x)$, then $g(0)=b+2a+a^2$.
$h(x)=g(x+1)-g(x)$, then $h(0)=2a$.
This can be extended to higher degree polynomials. This is related to the factorial and derivatives:
$f(0)=c$.
$f'(0)=b$.
$f''(0)=2a$.
Notice the coefficients:
$0!=1$
$1!=1$
$2!=2$