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. - The vertex of the parabola is at the origin $(0,0)$. - As $x$ increases or decreases, $y$ increases quadratically. 4. Intermediate work: - Calculate some points: 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. Plot these points and connect them smoothly to form a U-shaped curve. 6. The final graph is a parabola opening upwards with vertex at the origin.