Hello! The question is asking me to find the vertex, focus and directrix of the parabola, and sketch its graph.

y= (1/4) (x^2 -2x+5)

I tried putting aside the 1/4 for the time being and tried completing the square

y-5 = (x^2)-2x

y-3 = (x^2)-2x+2

y-3 = (x-1)^2

Plugging back in the 1/4 I got

y-3 = (1/4)(x-1)^2

With that, my vertex is (1, 3)

The book's answer is (1,1)

Please help me solve this problem, thanks!