1. The problem is to graph the function $y = x^2$. 2. The formula used is $y = x^2$, which is a quadratic function representing a parabola. 3. Important rules: The graph is symmetric about the y-axis because $x^2$ is an even function. 4. To plot, calculate values for $x$ and corresponding $y$: for example, $x = -2, -1, 0, 1, 2$ gives $y = 4, 1, 0, 1, 4$. 5. Plot these points and draw a smooth curve through them forming a U-shaped parabola opening upwards. 6. The vertex is at the origin $(0,0)$, which is the minimum point. 7. The parabola extends infinitely upwards as $x$ moves away from zero.