Question

{Please help me} Using the completing-the-square method, find the vertex of the function f(x) = 2x2 − 8x + 6 and indicate whether it is a minimum or a maximum and at what point. (2 points)

Maximum at (2, −2)
Minimum at (2, −2)
Maximum at (2, 6)
Minimum at (2, 6)

Answer 1

Answer: Minimum at (2,-2)

Proof of validity is shown below.

Answer 2

`f(x)=2x^2-8x+6=2(x^2-4x+3)\\\\=2(x^2-2x\cdot2+4-1)=2(x^2-2x\cdot2+2^2-1)\\\\=2[(x-2)^2-1]=2(x-2)^2+2\cdot(-1)=2(x-2)^2-2\\-------------------------\\f(x)=a(x-k)^2+h\to the\ vertex:(k;\ h)\\\\therefore\ the\ coordinates\ of\ the\ vertex:(2;-2)\\a=2\ to\ the\ minimum.\\\\Your\ answer:\boxed{Minimum:(2;-2)}`