1. **State the problem:** Identify the basic function from the given options and write the equation of the transformed graph. 2. **Analyze the graph shape:** The graph is an upward-opening parabola shifted right and down with vertex approximately at (2, -3). 3. **Identify the basic function:** An upward-opening parabola corresponds to the square function $$h(x) = x^2$$. 4. **Write the transformation formula:** The general form for horizontal and vertical shifts of $$h(x) = x^2$$ is: $$f(x) = (x - h)^2 + k$$ where $$h$$ is the horizontal shift and $$k$$ is the vertical shift. 5. **Apply the vertex coordinates:** Given vertex at (2, -3), the equation becomes: $$f(x) = (x - 2)^2 - 3$$ 6. **Final answer:** The basic function is the square function $$h(x) = x^2$$. The equation of the transformed graph is: $$f(x) = (x - 2)^2 - 3$$