The domain of a parabola refers to all the possible values of the independent variable (usually represented as x) for which the function is defined. For any parabola, whether it opens upwards or downwards, the domain is all real numbers. This can be expressed in interval notation as:
Domain: (-∞, ∞)
On the other hand, the range of a parabola depends on its orientation. If the parabola opens upwards, the range comprises all the real numbers greater than or equal to the minimum point of the vertex. Conversely, if the parabola opens downwards, the range includes all real numbers less than or equal to the maximum point of the vertex.
To summarize:
- If the parabola opens upwards: Range: [k, ∞), where k is the y-coordinate of the vertex.
- If the parabola opens downwards: Range: (-∞, k], where k is again the y-coordinate of the vertex.
Understanding the domain and range of a parabola is crucial in graphing the function and analyzing its behavior.