How may i select and omit legend elements recognized by Matlab on a problem?

Hi Everyone, i'd like to understand how to select legend elements from many legend elements that sequentially show on a scatter plot problem. The legend needs to show only these 4 elements, a red circle for the red scatter plot under 2 curves, a blue circle for a blue scatter plot above 2 curves, a black line for the 2 curves y(x) and d(c), and a black dot size 5 for y(x) = d(c) (an intersection). iow:

a 'r' for the string 'below both'; for elements 'm' and 'n' a 'b' for the string 'above either'; for elements 'o' and 'p' a 'k-' for the string 'f(x), g(x)'; for elements 'y(x)' and 'd(c)' a 'ko' for the string 'x_0', 'markerfacecolor', 'k', 'markeredgecolor', 'k', 'markersize', 5; for element 'd(q)'

A photo of desired result is attached and my Matlab program i wrote is:

problem 3c

clear all

rng(100);
N = 10^4;

x = 2*rand(1,N);
y = rand(1,N);

f = @(x) exp(-x.^2) - x./2;
x0 = 0.5;
q = fzero(f, x0);
[r,s] = find(f(q));

rng(100);

N = 10^4;
c = 2*rand(1,N);
d = rand(1,N);

i = find(y < exp(-x.^2) & y < x./2);
j = find(y >= exp(-x.^2)); 
l = find(d < c./2); 
k = find(d > c./2 & d < exp(-x.^2));

figure;
m = scatter(x(i), y(i), 1, 'r');
hold on;

n = scatter(c(l), d(l), 1, 'r');
o = scatter(x(j), y(j), 1, 'b');
p = scatter(c(k), d(k), 1, 'b');

x = 0:0.00020001:2;
y = @(x) exp(-x.^2);
c = 0:0.00020001:2;
d = @(c) c./2;

q;
d(q);

plot(x,y(x), 'k-', c,d(c), 'k-', q,d(q), 'ko', 'markeredgecolor',...
    'k', 'markerfacecolor', 'k', 'markersize', 5);

yaxis(0, 1, 0:1);
xaxis(0, 2, 0:1:2);
title('area under both curves');
ylabel('y');
xlabel('x');
legend('under both', 'above either', 'f(x), g(x)', 'x_0',...
    'location', 'n');

line([q,q], [d(q),0], 'linestyle', '--', 'color', 'k');
hold off;

How may i properly show the plot?