Final answer:
The domain of the parabola with vertex (-3, -5) that opens downward is all real numbers, and the range is all real numbers less than or equal to -5, expressed as (-∞, ∞) and (-∞, -5] in interval notation, respectively.
Step-by-step explanation:
The question pertains to a parabola with a given vertex (-3, -5) that opens downward. To find the domain and range in interval notation, we need to understand the characteristics of a parabola. Since the parabola opens downwards, its vertex is the highest point on the graph.
The domain of any parabola is all real numbers because for every x-value, there is a corresponding y-value. In interval notation, the domain is written as (-∞, ∞).
The range of a downward-opening parabola is all the y-values that are less than or equal to the y-coordinate of the vertex. Therefore, the y-values of the range do not go beyond -5. In interval notation, the range is written as (-∞, -5].