How to draw a small part of a parabola far from bend point using TikZ

I'd like to draw just part of a parabola (far from bend point) and then making a star shape by joining four of them. All examples of parabolas that I have seen contains the bend point. I think a solution for drawing a small part of parabola is clip trick but I don't know how to rotate and join them locally.

Precisely I want to use the following area enclosed by four parabola, to fill or clip using it.

\begin{tikzpicture}
\draw(0,0)  parabola [parabola height =3cm](4,0) node[midway, above]{aaaa};
\draw[rotate={180}](2,-2) parabola [parabola height =3cm](6,-2);
\draw[rotate=90](0,0) parabola [parabola height =3cm](4,0) ;
\draw[rotate={-90}](-2,-2) parabola [parabola height =3cm](2,-2);
\end{tikzpicture}

Also I have problem with the position of label on middle of parabola. Here is what I want: How to draw just colored region?

• could atleast show us a figure of what you desire and what you have tried so-far? – Raaja Feb 7 at 7:38
• You could use Bézier curves. There is also \pgfpathquadraticcurveto as a convenience wrapper to create quadratic Bézier curves (which internally are cubic, too). TikZ syntax would be to use controls with the correct control points. – Skillmon Feb 7 at 8:21
• Isn't the question clear enough? – C.F.G Feb 7 at 15:12
• @C.F.G: Draw a graphic on a napkin, add some descriptive arrows and notation to identify what you mean by "not the bend of a parabola", take a picture of it and upload it as part of your question. You really need to spoonfeed your audience if you want help in drawing something that requires some crystal ball gazing... – Werner Feb 7 at 16:16
• TikZ allows you to plot functions in any domain. Just try \draw plot[smooth,variable=\x,domain=2:4] ({\x},{\x*\x});. – user121799 Feb 7 at 16:27