This is how Bezier curve is drawn. It requires 4 points where (x1,y1) and (x4,y4) are starting and end points while (x2,y2) nand (x3,y3) are auxiliary points, constituting a rectangle-like form and a continuous Bezier curve is plotted within. If only (x2,y2) point is given, it will be repeated for (x3,y3) and the curve will be sharpter, instead of flatter (see the plots below). So the location of (x2,y2) and (x3,y3) do affect the curvature.
(x1,y1) .. controls (x2,y2) and (x3,y3) .. (x4,y4);

The plot on the right is newly added for comparison.
Code
\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw[semithick,->] (-2,0) -- (2,0) node[right] {$ x_1 $};
\draw[semithick,->] (0,-2) -- (0,2) node[left] {$ x_2 $};
\path[thick,blue,draw] (-2,2) .. controls (0,1) .. (0,0) .. controls (0,-1) .. (2,-2);
\path[thick,red,rotate=90,draw] (0,0) parabola (-2,-2);
\path[thick,blue,draw] (-2,2) .. controls (0,1) .. (0,0) .. controls (0,-1) .. (2,-2);
\end{tikzpicture}
\begin{tikzpicture}
\draw[semithick,->] (-2,0) -- (2,0) node[right] {$ x_1 $};
\draw[semithick,->] (0,-2) -- (0,2) node[left] {$ x_2 $};
\path[thick,yellow,draw] (-2,2) .. controls (0.65,1) and (0.65,-1) .. (-2,-2) node[right]{curve 1};
\path[thick,yellow,draw] (2,2) .. controls (-0.65,1) and (-0.65,-1) .. (2,-2)node[right]{curve 2};
\path[thick,cyan,draw] (2,2) node[right]{curve 3} .. controls (-0.65,0) .. (2,-2);
\path[thick,cyan,draw] (-2,2)node[right]{curve 4} .. controls (0.65,0) .. (-2,-2); % curve 3 and 4 are sharper because (x2,y2)=(x3,y3)
\end{tikzpicture}
\end{document}