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 vertex of the parabola is at the origin $(0,0)$. 4. The axis of symmetry is the vertical line $x=0$. 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 $(0,0)$ opening upwards.