[x,y]=meshgrid([-4:0.1:4]);
z = 4*y.^2 - x.^2;
surf(x,y,z)

Meshgrid creates a matrix x and y that look like this IF we used meshgrid([-4:1:4]), using 0.1 in the middle (the increment) would create much larger matrices no good for displaying

x =

-4    -3    -2    -1     0     1     2     3     4
-4    -3    -2    -1     0     1     2     3     4
-4    -3    -2    -1     0     1     2     3     4
-4    -3    -2    -1     0     1     2     3     4
-4    -3    -2    -1     0     1     2     3     4
-4    -3    -2    -1     0     1     2     3     4
-4    -3    -2    -1     0     1     2     3     4
-4    -3    -2    -1     0     1     2     3     4
-4    -3    -2    -1     0     1     2     3     4

y =

-4    -4    -4    -4    -4    -4    -4    -4    -4
-3    -3    -3    -3    -3    -3    -3    -3    -3
-2    -2    -2    -2    -2    -2    -2    -2    -2
-1    -1    -1    -1    -1    -1    -1    -1    -1
 0     0     0     0     0     0     0     0     0
 1     1     1     1     1     1     1     1     1
 2     2     2     2     2     2     2     2     2
 3     3     3     3     3     3     3     3     3
 4     4     4     4     4     4     4     4     4

Imagine looking down at the xy plane, along the z axis, the zeros of the x-matrix above would be the y-axis, and similarly the zeros in the y-matrix would be the x-axis.

Imagine overlaying the two matrices, and then plug each of the values at a given point into the equation, and that is your z at a given (x,y).

Use x.² and y.² instead of x² or y^2, the dot makes the power operation component-wise. x² squared would be telling Matlab to multiply two matrices together.