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!