The graph of $y = x^2$ is a parabola that opens upward. Here are some key features of this graph:

Key Characteristics:

1. Vertex: The lowest point is at $(0,0)$.
2. Axis of Symmetry: The vertical line $x = 0$ (the y-axis) is the axis of symmetry.
3. Shape: The parabola is U-shaped.
4. Domain: $(-\infty, \infty)$ (all real numbers).
5. Range: $[0, \infty)$ (all non-negative real numbers).

Would you like me to plot this graph for you? Let me know if you need any details!

Related Questions:

1. What is the effect of adding a constant to $y = x^2$, like $y = x^2 + 3$?
2. How does the graph change when we use $y = -x^2$ instead?
3. What is the vertex form of a quadratic equation?
4. How do we find the x-intercepts of a quadratic function?
5. Can we express $y = x^2$ in terms of a transformation from another function?

Tip:

The function $y = ax^2 + bx + c$ represents a general quadratic equation, where $a$ determines how wide or narrow the parabola is.