Question

The vertex of a parabola represented by f(x)=x^2 - 4x + 3 has coordinates (2,-1). Find the coordinates of the vertex of the parabola defined by g(x)=f(x-2). Explain how you arrived at your answer

Answer 1

$f(x)=x^2-4x+3$
a=1, b=-4, c=3
If the vertex has coordinates (2;-1)(p=2,q=-1) we can write vertex form of a parabola equation:
$f(x)=a(x-p)^2+q$
$f(x)=1(x-2)^2-1$

We need to put (x-2) at the place of (x) in f(x) equation to get g(x)
$g(x)=1[(x-2)-2]^2-1$
$g(x)=(x-2-2)^2-1$
$g(x)=(x-4)^2-1$
So:
p=4, q=-1

Vertex of the parabola defined by g(x)=f(x-2) has the vertex at $\boxed{(4;-1)}$

:)