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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...?
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    Your first equation is linear, the second is quadratic-they're quite different-https://en.wikipedia.org/wiki/Quadratic_equation – 2017-01-30
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    I do not know a name for $B_1$, but it describes how "broad" the parabola is and whether it has a global minimum or maximum. It is not the slope because the slope is not constant in the case of a parabola, but it is $2B_1x_0+B_2$ at position $x_0$ – 2017-01-30
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    @john I know it's linear vs quadratic, I just need the name for the coefficient with variable $x^2$ as in the coefficient for $x$ we call it 'slope' – 2017-01-30
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    I don't think it has a name beyond "leading coefficient", but that's not specific to quadratic equations. – 2017-01-30
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    @michaelMcGovern should i just describe as: $B_1$ and $B_2$ are the loading coefficients of $x^2$ and $x$ respectively, then? – 2017-01-30
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    @michaelMcGovern oh no just the $B_1$ is the leading coefficient. That doesn't sounds right though – 2017-01-30
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    If you edit your question to include several sentences on either side of where you have to name these things we may be able to provide suggestions appropriate in your context. (Please don't try to do that in a comment. Edit the question.) – 2017-01-30

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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:

$0!=1$

$1!=1$

$2!=2$