Question

determine whether the function y= x^2 cos x is even, odd, or neither

Answer 1

just follow the definition. a funtion f(x) is even if
\[\large f(-x)=f(x) \]
and is odd if
\[\large f(-x)=-f(x) \]

Answer 2

That approach certainly will work if applied correctly. Another approach would be to observe that both x^2 and cos x are even functions when taken separately, and to conclude that their product, (x^2)*cos x, is also an even function.