Questions: Question 32, 2.2.45 Part 1 of 2 Give the domain and range of the quadratic function whose graph is described. The vertex is (-6,-3) and the parabola opens up. The domain of f is . (Type your answer in interval notation.)

Question 32, 2.2.45 Part 1 of 2 Give the domain and range of the quadratic function whose graph is described. The vertex is (-6,-3) and the parabola opens up. The domain of f is . (Type your answer in interval notation.)
Transcript text: Question 32, 2.2.45 Part 1 of 2 Give the domain and range of the quadratic function whose graph is described. The vertex is $(-6,-3)$ and the parabola opens up. The domain of $f$ is $\square$ . (Type your answer in interval notation.)
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Solution

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Solution Steps

Step 1: Identify the Vertex and Direction of Opening

The given vertex is \((h, k) = (-6, -3)\) and the parabola opens up.

Step 2: Determine the Domain and Range

For a vertical parabola that opens up, the domain is always all real numbers, thus \(\text{Domain} = (-∞, ∞)\). The range depends on the direction of opening. Since it opens up, \(\text{Range} = ([-3, ∞))\).

Final Answer:

The domain of the parabola is (-∞, ∞) and the range is ([-3, ∞)), rounded to 0 decimal places if necessary.

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