The function g(x) = –x2 + 16x – 44 written in vertex form is g(x) = –(x – 8)2 + 20. which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = –x2 + 16x – 44?
the graph of f(x) = x2 is widened.
the graph of f(x) = x2 is shifted left 8 units.
the graph of f(x) = x2 is shifted down 44 units.
the graph of f(x) = x2 is reflected over the x-axis.

The graph of f(x) = x^2 is a parabola with vertex at the origin facing upwards. The graph of g(x) = -x^2 + 16x - 44 which is the same as the graph of -(x - 8)^2 + 20 is a parabola with vertex at (8, 20) facing downwards. Therefore, to obtain the graph of g(x) = -x^2 + 16x - 44 from the graph of f(x) = x^2, we perform the series of transformations which include: The graph of f(x) = x^2 is shifted right 8 units; the graph of f(x) = x^2 is shifted up 20 units and the graph of f(x) = x^2 is refrected over the x-axis. Therefore, the correct answer to the question is "The graph of f(x) = x^2 is refrected over the x-axis".