1. The problem is to graph the function $y = x^2$. 2. The function $y = x^2$ is a quadratic function, which forms a parabola opening upwards. 3. The general form of a quadratic function is $y = ax^2 + bx + c$. Here, $a = 1$, $b = 0$, and $c = 0$. 4. Important features of this graph include: - Vertex at $(0,0)$ - Axis of symmetry is the y-axis ($x=0$) - The parabola opens upwards because $a > 0$ 5. 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 $x = 2$, $y = 2^2 = 4$ 6. 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 with vertex at the origin, opening upwards.