One way: You could try an area plot with different colors and a transparency
p=0:0.001:0.25;
y3=(p + (1 - 4*p).^(1/2)/2).^2/2;
area(p,y3,'FaceColor','blue')
hold all
y5=(1/2)*(p+(1/2)*(1-4*p).^(1/2)).^2;
area(p,y5,'FaceColor','green')
hold all
p=0:0.001:0.5;
y1=2*p.^2;
area(p,y1,'FaceColor','red')
hold all
y7=p.^2;
area(p,y7,'FaceColor','cyan')
hold all
y2=(p-1/2).^2;
area(p,y2,'FaceColor','yellow')
hold all
alpha(0.5)
vline([((2)^(1/2)-1)/2,1/4],'black')