How to solve a quadratic equation coefficient a, b, c given 3 points

How can I solve for a quadratic equation's coefficients a, b, c of the form: y(x) = ax2 + bx +c? Given: y(0) = 1 y(200) = 0.5 y(500) = 0.2

Need simple Matlab code, no other tools. Thank you.

Answer 1

[Star Strider]

This is a linear equation (linear in the parameters), so you can use the mldivide,\ operator:

x = [0;  200;  500];
y = [1;  0.5;  2.0];

parms = [x.^2  x  ones(size(x))]\y

xv = linspace(min(x),  max(x))';

y_fit = [xv.^2  xv  ones(size(xv))]*parms;

figure(1)
plot(x, y, 'bp')
hold on
plot(xv, y_fit, '-r')
hold off
grid
text(75, 1.5, sprintf('y(x) = %8.3E\\cdotx^2 - %8.3E\\cdotx + %8.3E', abs(parms)))

You can also use the polyfit function.