For each of the following quadratic functions, determine if there is a minimum. If so, find the

Question:

For each of the following quadratic functions, determine if there is a minimum. If so, find the minimizer and the minimum value for the function.
(a) x2 - 2x y + 4y2 + x - 1
(b) 3x2 + 3xy + 3y2 - 2x - 2y + 4
(c) x2 + 5x y + 3y2 + 2x - y
(d) x2 + y2 + yz + z2 + x + y - z
(e) x2 + xy - y2-yz + z2- 3
(f) x2 + 5xz + y2 - 2yz + z2 + 2x - z-3
(g) x2 + x y + y2 + y z + z2 + z w + w2 - 2x - w