How to plot the region corresponding to an inequality?

I want to plot create the region plot for the inequality for . In Mathematica this can be done by

RegionPlot[y - x^2 >= 0, {x, -Sqrt[3], Sqrt[3]}, {y, 0, 3}, FrameLabel -> {"x", "y"}]

producing the following plot

How can one produce a similar plot in Matlab? The best I could do was using the spy function as follows

h = 0.01;
[x,y] = meshgrid(-sqrt(3):h:sqrt(3),0:h:3);
e = zeros(size(x)); 
Z = y-x.^2;
figure(1)
spy(Z >= e);
xlabel('x'), ylabel('y')

Here is another try

clear
h = 0.05;
[x,y] = meshgrid(-sqrt(3):h:sqrt(3),0:h:3);
ineq = y-x.^2 >= 0;    
f = double(ineq);
figure(2)
surf(x,y,f);
xlabel('x'), ylabel('y')
view(0,90) 

Any ideas? Thank you very much in advance.

Answer 1

[KSSV]

You are good to go with second method:

h = 0.01;

[x,y] = meshgrid(-sqrt(3):h:sqrt(3),0:h:3);
% e = zeros(size(x)); 
Z = y-x.^2;
idx = double(Z>=0) ; 
figure(1)

pcolor(x,y,idx)
shading interp 
xlabel('x'), ylabel('y')

[Dimitrios Anagnostou]

Thank you very much. I really appreciate it. Stupid question may be but how can I modify the blue color to white one and the yellow to blue (for instance)?

[KSSV]

h = 0.01;
[x,y] = meshgrid(-sqrt(3):h:sqrt(3),0:h:3);
% e = zeros(size(x)); 
Z = y-x.^2;
idx = double(Z>=0) ; 
figure(1)
% spy(Z >= 0);
% xlabel('x'), ylabel('y')
pcolor(x,y,idx)

shading interp 
cmap = [255 255 255;0 0 255]/255 ;
colormap(cmap)

[Andrew Sol]

How can I add a grid to this plot?