Question

The vertex of a parabola represented by f(x)=x^2-4x+3 has coordinates of (2,-1). Find the coordinates of the vertex of the parabola defined by g(x)=f(x-2). Explain how you arrived to your answer.
My question: Would you move the parabola represented by f(x) 2 spaces to the right to get the parabola represented by g(x)?

Answer 1

yes,
the new vertex will be (4,-1)

proof:
f(x-2) = (x-2)^2 - 4(x-2) + 3
= x^2 - 4x + 4 - 4x + 8 + 3
= x^2 - 8x + 15
= g(x)
vertex of g(x) = -b/(2a)
= 8/2 = 4
g(4) = 4^2 - 8(4) + 15 = -1
vertex is (4,-1)