1. **State the problem:** We need to identify and compare the graph of the function $$n(x) = \frac{1}{3}x^2 - 5$$ with the graph of $$f(x) = x^2$$. 2. **Recall the base function:** The graph of $$f(x) = x^2$$ is a parabola opening upwards with vertex at the origin $$(0,0)$$, symmetric about the y-axis. 3. **Analyze the transformation:** The function $$n(x) = \frac{1}{3}x^2 - 5$$ can be seen as a transformation of $$f(x)$$: - The coefficient $$\frac{1}{3}$$ in front of $$x^2$$ causes a vertical shrink by a factor of $$\frac{1}{3}$$, making the parabola wider. - The $$-5$$ shifts the graph vertically downward by 5 units. 4. **Vertex of $$n(x)$$:** Since $$f(x)$$ has vertex at $$(0,0)$$, the vertex of $$n(x)$$ is at $$(0, -5)$$. 5. **Summary:** The graph of $$n(x)$$ is a parabola opening upwards, symmetric about the y-axis, vertically shrunk by a factor of $$\frac{1}{3}$$ compared to $$f(x)$$, and shifted down 5 units. **Final answer:** The graph of $$n(x) = \frac{1}{3}x^2 - 5$$ is a vertically shrunk (by factor $$\frac{1}{3}$$) and vertically translated (down 5 units) parabola compared to $$f(x) = x^2$$, with vertex at $$(0, -5)$$.