y=x^2

The equation \( y = x^2 \) represents a quadratic function. Here are some key details about this function:

1. Graph: The graph of \( y = x^2 \) is a parabola that opens upwards. The vertex of the parabola is at the origin point (0, 0).

2. Shape: The parabola is symmetric about the y-axis. This means that for any point (x, y) on the graph, the point (-x, y) will also be on the graph.

3. Intercepts:

   • Y-intercept: The parabola intersects the y-axis at (0, 0).
   • X-intercepts: The parabola intersects the x-axis at (0, 0) as well, since the only solution to \( x^2 = 0 \) is \( x = 0 \).

4. Domain: The domain of the function is all real numbers \( (-\infty, \infty) \) because you can input any real number into \( x^2 \).

5. Range: The range of the function is all non-negative real numbers \([0, \infty)\) since \( y = x^2 \) is always greater than or equal to 0.

6. Vertex: The vertex is at the point (0, 0), which is the minimum point of the function.

7. Axis of Symmetry: The axis of symmetry is the line \( x = 0 \).

8. Behavior: As \( x \) approaches positive or negative infinity, \( y \) also approaches infinity.

If you have any specific questions about this function or need help with related problems, feel free to ask!