Rewrite the quadratic function in vertex form by completing the square:
f(x) = x2 - 4x + 3

f(x) = (x - 2)² - 1

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Given

f(x) = x² - 4x + 3

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 4x

f(x) = x² + 2(- 2)x + 4 - 4 + 3

     = (x - 2)² - 1

f(x) = (x - 2)^2 - 1

Step-by-step explanation:

f(x) = x^2 - 4x + 3 is the proper way in which to write this; the " ^ " signifies "exponentiation," where x2 is meaningless.

To complete the square:

Rewrite f(x) = x^2 - 4x + 3   as   f(x) = x^2 - 4x                                       + 3

Take half of the coefficient of x (end result is -2), square this end result and add, then subtract, it from  f(x) = x^2 - 4x:

f(x) = x^2 - 4x + (-2)^2 - (-2)^2 + 3, or

f(x) = x^2 - 4x + 4 - 4 + 3

Rewrite x^2 - 4x + 4 as the square of x - 2:  

f(x) = (x - 2)^2 - 1

This is the equation in vertex form; the vertex is (2, -1).