%
% C. Talarico
% file: plotcomplexquadratic.m
%

clear all; close all; clc;
syms x;

figure
hold on
a = 1; b = 2; c = 5;
y = a*x^2 + b*x + c;
r = solve(y == 0, x);
r_12 = vpa(r)
Dy = diff(y,x);
mm = solve(Dy == 0, x);
x_min = vpa(mm)
h1 = ezplot(y);
set(h1, 'color','m','linewidth',1);
y1_str = char(y);

a= -1; b= -2; c= -5;
y = a*x^2 + b*x + c;
r = solve(y == 0, x);
r_12 = vpa(r)
Dy = diff(y,x);
mm = solve(Dy == 0, x);
x_max = vpa(mm)
f1 = ezplot(y);
set(f1, 'color','b','linewidth',1);
y2_str = char(y);

ax = gca;
set(ax,'Fontsize',14, 'FontName', 'Monospace', 'Fontweight', 'Normal');
xlabel('x', 'Fontsize', 16);
title('y = a x^2 + b x + c', 'Fontsize', 18);
ylim([-50 +50]);
legend(y1_str, y2_str, 'location','Best');

line([-10 10],[0 0],'color','r','LineStyle',':', 'linewidth',2);
line([0 0],[-50 +50], 'color', 'k', 'LineStyle',':', 'linewidth',2);

hold off;
disp('---------------------------------');


figure;
fig = plot(r_12, 'X', 'MarkerSize',18,'LineWidth',2);
ax = gca;
set(ax,'Fontsize',14, 'FontName', 'Monospace', 'Fontweight', 'Normal');
xlabel('real axis','Fontsize', 16);
ylabel('imaginary axis','Fontsize', 16);
title('s-plane roots','Fontsize', 18);

line([-10 10],[0 0],'color','k','LineStyle','-', 'linewidth',1);
line([0 0],[-10 +10], 'color', 'k', 'LineStyle','-', 'linewidth',1);

str = sprintf(' y = %s \n y = %s ', y1_str, y2_str);
text(1,6, str, 'fontSize', 16, 'FontWeight', 'Bold', ...
    'EdgeColor','k', 'linewidth',1, 'backgroundcolor','y');
grid on;

figure
hold on;
a = -1; b = 2; c = -5;
y = a*x^2 + b*x + c;
r = solve(y==0, x);
r_12 = vpa(r)
Dy = diff(y,x);
mm = solve(Dy == 0, x);
x_max = vpa(mm)
ezplot(y);
h2 = ezplot(y);
set(h2, 'color','m','linewidth',1);
y1_str = char(y);

a= 1; b= -2; c= 5;
y = a*x^2 + b*x + c;
r = solve(y == 0, x);
r_12 = vpa(r)
Dy = diff(y,x);
mm = solve(Dy == 0, x);
x_min = vpa(mm)
f2 = ezplot(y);
set(f2, 'color','b','linewidth',1);
y2_str = char(y);

ax = gca;
set(ax,'Fontsize',14, 'FontName', 'Monospace', 'Fontweight', 'Normal');
xlabel('x', 'Fontsize', 16);
title('y = a x^2 + b x + c', 'Fontsize', 18);
ylim([-50 +50]);
legend(y1_str, y2_str, 'location','Best');

line([-10 10],[0 0],'color','r','LineStyle',':', 'linewidth',2)
line([0 0],[-50 +50], 'color', 'k', 'LineStyle',':', 'linewidth',2);

hold off;
disp('---------------------------------');

figure;
fig = plot(r_12, 'X', 'MarkerSize',18,'LineWidth',2);
ax = gca;
set(ax,'Fontsize',14, 'FontName', 'Monospace', 'Fontweight', 'Normal');
xlabel('real axis','Fontsize', 16);
ylabel('imaginary axis','Fontsize', 16);
title('s-plane roots','Fontsize', 18);

line([-10 10],[0 0],'color','k','LineStyle','-', 'linewidth',1);
line([0 0],[-10 +10], 'color', 'k', 'LineStyle','-', 'linewidth',1);

str = sprintf(' y = %s \n y = %s ', y1_str, y2_str);
text(1,6, str, 'fontSize', 16, 'FontWeight', 'Bold', ...
    'EdgeColor','k', 'linewidth',1, 'backgroundcolor','y');
grid on;


figure
hold on
a = -1; b = 2; c = 5;
y = a*x^2 + b*x + c;
r = solve(y == 0, x);
r_12 = double(vpa(r,4))
r_1 = complex(r_12(1),0);
r_2 = complex(r_12(2),0);
r_12 = [r_1, r_2]
Dy = diff(y,x);
mm = solve(Dy == 0, x);
x_max = vpa(mm)
h1 = ezplot(y);
set(h1, 'color','m','linewidth',1);
y1_str = char(y);

a= 1; b= -2; c= -5;
y = a*x^2 + b*x + c;
r = solve(y == 0, x);
r_12 = double(vpa(r,4))
r_1 = complex(r_12(1),0);
r_2 = complex(r_12(2),0);
r_12 = [r_1, r_2]
Dy = diff(y,x);
mm = solve(Dy == 0, x);
x_min = vpa(mm)
f1 = ezplot(y);
set(f1, 'color','b','linewidth',1);
y2_str = char(y);

ax = gca;
set(ax,'Fontsize',14, 'FontName', 'Monospace', 'Fontweight', 'Normal');
xlabel('x', 'Fontsize', 16);
title('y = a x^2 + b x + c', 'Fontsize', 18);
ylim([-50 +50]);
legend(y1_str, y2_str, 'location','Best');

line([-10 10],[0 0],'color','r','LineStyle',':', 'linewidth',2);
line([0 0],[-50 +50], 'color', 'k', 'LineStyle',':', 'linewidth',2);

hold off;
disp('---------------------------------');


figure;
fig = plot(r_12, 'X', 'MarkerSize',18,'LineWidth',2);
ax = gca;
set(ax,'Fontsize',14, 'FontName', 'Monospace', 'Fontweight', 'Normal');
xlabel('real axis','Fontsize', 16);
ylabel('imaginary axis','Fontsize', 16);
title('s-plane roots','Fontsize', 18);

line([-10 10],[0 0],'color','k','LineStyle','-', 'linewidth',1);
line([0 0],[-10 +10], 'color', 'k', 'LineStyle','-', 'linewidth',1);

str = sprintf(' y = %s \n y = %s ', y1_str, y2_str);
text(1,6, str, 'fontSize', 16, 'FontWeight', 'Bold', ...
    'EdgeColor','k', 'linewidth',1, 'backgroundcolor','y');
grid on;
hold off;


figure
hold on
a = -1; b = -2; c = 5;
y = a*x^2 + b*x + c;
r = solve(y == 0, x);
r_12 = double(vpa(r,4))
r_1 = complex(r_12(1),0);
r_2 = complex(r_12(2),0);
r_12 = [r_1, r_2]
Dy = diff(y,x);
mm = solve(Dy == 0, x);
x_max = vpa(mm)
h1 = ezplot(y);
set(h1, 'color','m','linewidth',1);
y1_str = char(y);

a= 1; b= 2; c= -5;
y = a*x^2 + b*x + c;
r = solve(y == 0, x);
r_12 = double(vpa(r,4))
r_1 = complex(r_12(1),0);
r_2 = complex(r_12(2),0);
r_12 = [r_1, r_2]
Dy = diff(y,x);
mm = solve(Dy == 0, x);
x_min = vpa(mm)
f1 = ezplot(y);
set(f1, 'color','b','linewidth',1);
y2_str = char(y);

ax = gca;
set(ax,'Fontsize',14, 'FontName', 'Monospace', 'Fontweight', 'Normal');
xlabel('x', 'Fontsize', 16);
title('y = a x^2 + b x + c', 'Fontsize', 18);
ylim([-50 +50]);
legend(y1_str, y2_str, 'location','Best');

line([-10 10],[0 0],'color','r','LineStyle',':', 'linewidth',2);
line([0 0],[-50 +50], 'color', 'k', 'LineStyle',':', 'linewidth',2);

hold off;
disp('---------------------------------');


figure;
fig = plot(r_12, 'X', 'MarkerSize',18,'LineWidth',2);
ax = gca;
set(ax,'Fontsize',14, 'FontName', 'Monospace', 'Fontweight', 'Normal');
xlabel('real axis','Fontsize', 16);
ylabel('imaginary axis','Fontsize', 16);
title('s-plane roots','Fontsize', 18);

line([-10 10],[0 0],'color','k','LineStyle','-', 'linewidth',1);
line([0 0],[-10 +10], 'color', 'k', 'LineStyle','-', 'linewidth',1);

str = sprintf(' y = %s \n y = %s ', y1_str, y2_str);
text(1,6, str, 'fontSize', 16, 'FontWeight', 'Bold', ...
    'EdgeColor','k', 'linewidth',1, 'backgroundcolor','y');
grid on;
hold off;