I need a contour plot of the function $f(x,y) = (x-1)^4 + (2x+y)^2$. Using Mathematica, I get
I thought this looks strange. The contour plot is supposed to show ellipses. After all, this is what the graph of $f$ looks like (elliptical paraboloid) using GeoGebra
I thought that I was doing something wrong with ContourPlot. But then I used Plot3D on that same function $f$, and I got this
So I don't know what's going on here. I don't understand why Plot3D doesn't generate the elliptical paraboloid that it is supposed to. But what I really need is the contour plot showing the ellipses.
Thanks in advance for any help, and sorry if the images in the body of the questions are too big.