Use transformations of the graph of f(x)=x^2 to determine the graph of the given function. g(x)=4(x-2)^2 Select all the transformations that are needed to graph the given function using f(x)=x^2 A. Shift the graph 2 units up B. Reflect the graph about the x-axis. C. Reflect the graph about the y-axis. D. Stretch the graph horizontally by a factor of 4 E. Shrink the graph vertically by a factor of 4 F. Stretch the graph vertically by a factor of 4 G. Shrink the graph horizontally by a factor of 4.

To determine the transformations needed to graph the function using the graph of , we can compare the given function with the standard form of a quadratic function, which is , where represents the vertex of the parabola.Comparing with the standard form, we can see that:- The coefficient 4 in front of indicates a vertical stretch by a factor of 4.- The term inside the squared parentheses indicates a horizontal shift 2 units to the right.- There is no constant term added or subtracted outside the squared parentheses, so there is no vertical shift.Therefore, the transformations needed to graph the function using are:- Shift the graph 2 units to the right (option D)- Stretch the graph vertically by a factor of 4 (option F)So, the correct options are D and F.