The equation you provided is a simple quadratic equation: $y = x^2$. Here's a breakdown of its key characteristics:

Key Characteristics:

1. Type of Function: This is a quadratic function, meaning its graph will be a parabola.
2. Vertex: The vertex of the parabola is at $(0,0)$, since there are no additional constants or linear terms in the equation.
3. Symmetry: The graph is symmetric about the y-axis because the function is even (i.e., $f(x) = f(-x)$).
4. Shape of the Graph: The parabola opens upwards since the coefficient of $x^2$ is positive.
5. Intercepts:
   • x-intercept: $x = 0$ (since $y = 0$ when $x = 0$).
   • y-intercept: $y = 0$ (since $y = 0$ when $x = 0$).

Would you like me to go into more details on the graph, or the applications of quadratic functions?

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