where <math>~ x = [x_1, x_2] \in V </math> and {{mvar|c}}{{sub|1}} and {{mvar|c}}{{sub|2}} are constants. If {{nobr| {{mvar|c}}{{sub|1}} > 0 }} and {{nobr| {{mvar|c}}{{sub|12}} > 0 ,}} the quadratic form {{mvar|Q}} is positive-definite, so ''Q'' evaluates to a positive number whenever <math>\; [x_1,x_2] \neq [0,0] ~.</math> If one of the constants is positive and the other is 0, then {{mvar|Q}} is positive semidefinite and always evaluates to either 0 or a positive number. If {{nobr| {{mvar|c}}{{sub|1}} > 0 }} and {{nobr| {{mvar|c}}{{sub|2}} < 0 ,}} or vice versa, then {{mvar|Q}} is indefinite and sometimes evaluates to a positive number and sometimes to a negative number. If {{nobr| {{mvar|c}}{{sub|1}} < 0 }} and {{nobr| {{mvar|c}}{{sub|2}} < 0 ,}} the quadratic form is negative-definite and always evaluates to a negative number whenever <math>\; [x_1,x_2] \neq [0,0] ~.</math> And if one of the constants is negative and the other is 0, then {{mvar|Q}} is negative semidefinite and always evaluates to either 0 or a negative number.
In general a quadratic form in two variables will also involve a cross-product term in {{mvar|x}}{{sub|1}}·{{mvar|x}}{{sub|2}}:
