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. - The vertex is at the origin $(0,0)$. - The parabola opens upwards because the coefficient of $x^2$ is positive. 4. To plot the graph, calculate some points: - When $x = -2$, $y = (-2)^2 = 4$. - When $x = -1$, $y = (-1)^2 = 1$. - When $x = 0$, $y = 0^2 = 0$. - When $x = 1$, $y = 1^2 = 1$. - When $x = 2$, $y = 2^2 = 4$. 5. Plot these points and draw a smooth curve through them to form the parabola. Final answer: The graph of $y = x^2$ is a parabola opening upwards with vertex at $(0,0)$ and symmetric about the y-axis.