1. The problem is to analyze the function $$y = (2x)^2 - 2$$ and describe the transformations from the base function $$y = x^2$$. 2. Start with the base function $$y = x^2$$, which is a parabola opening upwards with vertex at the origin (0,0). 3. The given function is $$y = (2x)^2 - 2 = 4x^2 - 2$$. 4. The factor 4 in front of $$x^2$$ means the parabola is vertically stretched by a factor of 4 compared to $$y = x^2$$. 5. The $$-2$$ at the end means the graph is translated downward by 2 units. 6. There is no horizontal translation or horizontal stretch/shrink because the input to the square is $$2x$$, which affects horizontal scaling, but since it is squared, it results in vertical stretch. 7. To summarize, the graph is a vertical stretch by 4 and a downward translation by 2 units from $$y = x^2$$. 8. Therefore, the correct description is: **Start with** $$y = x^2$$. **Vertically stretch by a factor of** 4. **Translate down** 2 units. This matches option D except for the direction of translation (D says translate down, which is correct), but D mentions horizontally shrink which is not correct here because the horizontal scaling by 2 inside the function results in vertical stretch by 4. Hence, the best match is option D with the correct interpretation. Final answer: The graph is a vertical stretch by 4 and translated down 2 units from $$y = x^2$$.