Question

s the anyone know how can i rewrite this f(x)=x^2−2x+3 in the form of f(x)=a(x-h)^2+k

Answer 1

you "complete the square"

using the idea that
(x + g)(x+g)= x^2 +2g x + g^2

match your expression
x^2 +2g x + g^2
x^2 -2 x + 3

specifically, match the 2nd terms:
2g x = -2 x
you find g= -1

and g^2 = 1

write
x^2 - 2 x + 1 - 1 + 3
I added and subtracted 1

(x^2-2x + 1) + 3-1
(x-1)^2 + 2