The Plot you provided puts the axis on the right side (for me on my setup anyway). But the general answer is that you can control placement of the axes by setting the axes origin:
Plot[x^2 + 1, {x, -10, 10}, PlotPoints -> 100, MaxRecursion -> 0,
Background -> White, AxesLabel -> {x, y}, PlotRange -> {-10, 10},
AxesOrigin -> {10, 0}]
I changed {x,-10,0}
to {x,-10,10}
so you could see a definite difference.
Update
Based on your comment, maybe this is what you want (or maybe the inverse of this):
With[
{n = 4, p = 30},
Plot[(n x/p)^2 + 1, {x, -10, 10}]]
Or maybe a parametric plot?
With[
{n = 4, p = 30},
ParametricPlot[{t p/n, 1 + t^2}, {t, -10, 10}]]
The With isn't necessary, I was just trying to clarify and explicitly use n and p from your update.
{x,-10,0}
to be whatever you want it to be. You'll have to change/eliminate the PlotRange option also. $\endgroup$