# Lab Solutions

## Introduction

clear all;
close all;

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## Problem #1

xdata = [-3.2; 5.4];
ydata = [1.2; -4.3];

V = vander(xdata);
a = V\ydata;
fprintf('Slope is       %16.8f\n',a(1));
fprintf('y-intercept is %16.8f\n',a(2));
xs = linspace(-4,6,20);
ys = a(1)*xs + a(2);

plot(xs,ys,'r','linewidth',2);
hold on;
plot(xdata,ydata,'k.','markersize',30);
plot(0,a(2),'b.','markersize',30);
plot([0 0],get(gca,'ylim'),'k--');
xlim = get(gca,'xlim');
plot(xlim,[a(2) a(2)],'k--');
snapnow;
Slope is            -0.63953488
y-intercept is      -0.84651163


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## Problem #2

close all;
xdata = [-3.2; 1.2; 6.1];
ydata = [4.5; 6.1; -3.4];

V = vander(xdata);
a = V\ydata;
xmax = -a(2)/(2*a(1));
ymax = polyval(a,xmax);
fprintf('Maximum value is at x = %16.8f\n',xmax);
fprintf('Maximum value is    y = %16.8f\n',ymax);

xs = linspace(-4,7,100);
ys = polyval(a,xs);

plot(xs,ys,'r','linewidth',2);
hold on;
plot(xdata,ydata,'k.','markersize',30);
ylim = get(gca,'ylim');
plot([xmax xmax],ylim,'k--');
plot(xmax,ymax,'b.','markersize',30);
xlim = get(gca,'ylim');
plot(xlim,[ymax,ymax],'k--');
axis([-4 7 ylim]);
snapnow;
Maximum value is at x =      -0.26559226
Maximum value is    y =       6.63177314


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