Answer: See below
Explanation:
Rewrite in vertex form
f(x) = 2x^2-8x+1
f(x) = 2(x^2-4x) + 1
f(x) + ? = 2(x^2 -4x +?) + 1
To find ?, calculate (b/2)^2, in this case, b is 2
(2/2)^2
= 4
f(x) + 4 = 2(x^2 -4x +4) + 1
f(x) + 2*4 = 2(x^2 -4x +4) + 1
f(x) = 2(x-2)^2 -7
Vertex: (2, -7)
Minimum: (2 -7) - Same as the vertex