solve quadratic for max & min

how to solve this quadratic equation for Max & Min values:

A1*x1^2 + B1*x1*x2 + C1*x2^2 + D1*x1 + E1*x2 + F1

can't find a proper explanation. Please!

Answer 1

[Walter Roberson]

If A1 is negative, then for every finite x2, the mininum is at x1 = +/- infinity.

If C1 is negative, then for every finite x1, the minimum is at x2 = +/- infinity.

Otherwise, for every finite x1 and finite x2, the minimum is at

x1 = (B1*E1-2*C1*D1)/(-B1^2+4*C1*A1)
x2 = -(2*A1*E1-D1*B1)/(-B1^2+4*C1*A1)

If A1 and C1 are opposite signs, then when x1 and x2 are both infinite, the minimum is undefined.

[zaxven]

thanks!but now if i do mesh grid i get an empty matrix. plus contour doesn't plot.

Error using contour : Z must be size 2x2 or greater.

[x1 x2] = meshgrid(x1min:delta:x1max, x2min:delta:x2max);

%% delta = b^2-4ac %% assuming minimums to be -inf

Z = a*x1.^2 + b*x1.*x2 + c*x2.^2 + d*x1 + e*x2 + f;

contour(z1,z2,Z);

[Walter Roberson]

What values do you have for x1min, x1max, x2min, x2max, and delta? You might be in a situation where one of x1min:delta:x1max or x2min:delta:x2max are empty, in which case Z would come out empty.

Also, what are z1 and z2 ?