Questions: Give the domain and range of the quadratic function whose graph is described. The vertex is (-8,-7) and the parabola opens down.

Solution Steps

To determine the domain and range of a quadratic function, we need to consider the vertex and the direction in which the parabola opens. Since the parabola opens downwards, the domain is all real numbers, and the range is all values less than or equal to the y-coordinate of the vertex.

The vertex of the quadratic function is given as \( (-8, -7) \). This point represents the maximum value of the function since the parabola opens downwards.

The domain of a quadratic function is always all real numbers. Therefore, we can express the domain as: \[ \text{Domain} = \mathbb{R} \]

Since the parabola opens downwards, the range consists of all values less than or equal to the y-coordinate of the vertex. Thus, the range can be expressed as: \[ \text{Range} = \{ y \in \mathbb{R} \mid y \leq -7 \} \]

Final Answer