# How do I plot a polynomial equation and set of x-y coordinates on the same graph?

8 views (last 30 days)
Deleted User on 10 May 2024
Edited: John Kelly on 20 May 2024
I am trying to plot a polynmial and some x-y coordinates on the same graph. I need the coordinates to be visible and the lines to be distingushable from one another (eg. different colors).
Here is the measured data.
coefficients = [0.6252 -0.4165 0.1311 -0.0163 0.0009,-0.0000]
x = [2 5 8 11 14 20];
y = [0.20 0.29 0.44 0.50 0.66 0.56];

Sam Chak on 10 May 2024
Edited: Sam Chak on 10 May 2024
Edit: Your original polynomial coefficients are truncated. So, the polynomial cannot produce an accurate result.
%% data
x = [2 5 8 11 14 20];
y = [0.20 0.29 0.44 0.50 0.66 0.56];
%% polynomial coefficients
coefficients = [0.6252 -0.4165 0.1311 -0.0163 0.0009 -0.0000];
p = fliplr(coefficients)
p = 1x6
0 0.0009 -0.0163 0.1311 -0.4165 0.6252
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format long
p = polyfit(x, y, numel(x)-1)
p = 1x6
-0.000018175582990 0.000901920438957 -0.016287722908091 0.131052812071305 -0.416499314128809 0.625240054869418
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%% points generated by polynomial
xx = linspace(x(1), x(end), 181);
yy = polyval(p, xx);
%% plot results
plot(x, y, 'o', 'markersize', 10), hold on
plot(xx, yy), grid on, xlabel('x'), xlabel('y')
legend('data', 'polynomial', 'location', 'northwest')
Deleted User on 11 May 2024
Thank you for that! Sorry to bother you, but I have another question. I’m trying to plot another point on the polynomial. I know the x coordinate is 17.5, but I don’t know the y coordinate. Is there a way I could plot the x coordinate on the polynomial and use the information from the graph to figure out the y coordinate? This coordinate needs to be distinguished from the points (eg. different colour).
Sam Chak on 11 May 2024
Edited: John Kelly on 20 May 2024
Hi
You can use the polyval() command in this case.
%% data
x = [2 5 8 11 14 20];
y = [0.20 0.29 0.44 0.50 0.66 0.56];
%% polynomial coefficients
p = polyfit(x, y, numel(x)-1)
p = 1x6
-0.0000 0.0009 -0.0163 0.1311 -0.4165 0.6252
<mw-icon class=""></mw-icon>
<mw-icon class=""></mw-icon>
%% points generated by polynomial
xx = linspace(x(1), x(end), 181);
yy = polyval(p, xx);
%% find y coordinate with given x coordinate
xpt = 17.5;
ypt = polyval(p, xpt)
ypt = 0.9379
%% plot results
plot(x, y, 'o', 'markersize', 10), hold on
plot(xx, yy), grid on, xlabel('x'), ylabel('y')
plot(xpt, ypt, 'p', 'markersize', 10, 'color', "#7E2F8E"), hold off
legend('data', 'polynomial', 'point', 'location', 'northwest')

### More Answers (1)

KSSV on 10 May 2024
x = [2 5 8 11 14 20];
y = [0.20 0.29 0.44 0.50 0.66 0.56];
p = polyfit(x,y,3) ;
yi = polyval(p,x) ;
figure
hold on
plot(x,y,'r')
plot(x,yi,'b')
legend('data points','polynomial fit')

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