f(x)=2x^2-4x+1 written in standard form

Answer 1

2x^2 -4x + 1 complete the square

2(x^2 -2x + 1) + 1 - 2

2(x-1)^2 -1 is a parabola with vertex (1,-1) = minimum point of an upward opening parabola

general standard equation for a vertical parabola is ax^2 + bx + c with a=2, b =-4 and c= 1

or in standard vertex form a(x-h)^2 + k where (h,k) is the vertex = (1,-1)