How can I plot $f(x, y) = x^2 + y^2$

Question

I want to plot $f(x, y) = x^2 + y^2$? I can plot functions of a single variable but I don't know how to plot multivariable function.

Answer 1

Your plot has three dimensions. You can plot it in perspective, in contour lines, or in various other representations. Alpha gives the following:

Answer 2

The graph of this function will be a surface in space. Above the point $(x,y)$ in the plane it has height $f(x,y)$.

https://www.mathcurve.com/surfaces.gb/paraboloidrevolution/paraboloidrevolution.shtml

Answer 3

In order to sketch this surface we need to consider $$z=x^2+y^2=(\text{distance of }(x,y)\text{ from }(0,0))^2$$ So this is intuitively equivalent to the surface created by rotating the graph of $z=x^2$ about the $z$ axis.

Answer 4

Since the function $f(x,y)=x^2+y^2$ is from $\mathbb{R^2}$ to $\mathbb{R}$ we clearly need to visualise it in $\mathbb{R^{2+1}}$,and since the domain is $\mathbb{R^{2}}$ the graph will be a surface!! If you want to visualise any such fuction you can use https://www.wolframalpha.com/ and your graph looks like https://www.wolframalpha.com/input/?i=plot+x%5E2%2By%5E2

PS:I would suggest you to use LaTeX to type your questions.