Questions: Give the domain and range of the quadratic function whose graph is described. The vertex is (-3,-1) and the parabola opens down. The domain of f is (Type your answer in interval notation.)

Give the domain and range of the quadratic function whose graph is described. The vertex is (-3,-1) and the parabola opens down.

The domain of f is (Type your answer in interval notation.)

Transcript text: Give the domain and range of the quadratic function whose graph is described. The vertex is $(-3,-1)$ and the parabola opens down. The domain of $f$ is $\square$ (Type your answer in interval notation.)

Solution

Solution Steps

Step 1: Identify the Vertex and Direction of Opening

The given vertex is $(h, k) = (-3, -1)$ and the parabola opens down.

Step 2: Determine the Domain and Range

For a vertical parabola that opens down, the domain is always all real numbers, thus $\text{Domain} = (-∞, ∞)$. The range depends on the direction of opening. Since it opens down, $\text{Range} = ((-∞, -1])$.