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)?

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

    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)

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