So the way you check if a function is a perfect square is by taking the discriminant of the function.

D=b^{2}-4ac

y=ax^{2}+bx+c

The equation above will give you the discriminant of a quadratic function. A quadratic function is a perfect quadratic trinomial, so long that the Discriminant equals 0. (D=0)

For the y^{2}+16y-64=0

D=16^{2}-4*(1)*(-64)=256+256=512

∴D=512 and D≠0

∴The function is not a perfect quadratic trinomial.