1. **Problem:** Sketch a rough graph of the function $$y = x^2$$. 2. **Formula and Explanation:** The function $$y = x^2$$ is a quadratic function representing a parabola. - The graph is symmetric about the y-axis. - The vertex (minimum point) is at the origin $$(0,0)$$. - As $$x$$ increases or decreases, $$y$$ increases quadratically. 3. **Key points to plot:** - At $$x=0$$, $$y=0^2=0$$. - At $$x=1$$, $$y=1^2=1$$. - At $$x=-1$$, $$y=(-1)^2=1$$. - At $$x=2$$, $$y=2^2=4$$. - At $$x=-2$$, $$y=(-2)^2=4$$. 4. **Shape description:** - The graph is a U-shaped curve opening upwards. - It passes through points $$(0,0), (1,1), (-1,1), (2,4), (-2,4)$$. 5. **Summary:** - The parabola $$y = x^2$$ has vertex at the origin. - It is symmetric about the y-axis. - The graph opens upwards and gets steeper as $$|x|$$ increases. Final answer: The graph of $$y = x^2$$ is a parabola with vertex at $$(0,0)$$ opening upwards.