Question

The vertex of the 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

The graph of f(x-2) is the graph of f(x) shifted right by 2 units.
The x-coordinate of the vertex of f(x-2) is the x-coordinate of the vertex of f(x) plus 2, so it is 2+2=4.
The y-coordinate of the vertex doesn't change.

The vertex of the parabola defined by g(x)=f(x-2) is (4,-1).