1. The problem is to graph the function $y = x^2$. 2. The formula for this function 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 $(0,0)$. - As $x$ increases or decreases, $y$ increases quadratically. 4. Intermediate work: - For $x = -2$, $y = (-2)^2 = 4$. - For $x = -1$, $y = (-1)^2 = 1$. - For $x = 0$, $y = 0^2 = 0$. - For $x = 1$, $y = 1^2 = 1$. - For $x = 2$, $y = 2^2 = 4$. 5. Explanation: - Plotting these points shows the parabola shape. - The graph opens upwards and is U-shaped. Final answer: The graph of $y = x^2$ is a parabola with vertex at $(0,0)$ opening upwards.