Identify the vertex, axis of symmetry, domain, and range of a parabola. Select one: Vertex: $$ (-1.5,-7.75) $$; Axis of symmetry: $$ x=-1.5 $$; Domain: $$ x \in R $$; Range: $$ y \geq-7.75 $$ Vertex: $$ (-9,1) $$; Axis of symmetry: $$ x=-3 $$; Domain: $$ x \in R ; $$ Range: $$ y \geq 1 $$ Vertex: $$ (1.5,7.75) $$; Axis of symmetry: $$ x=1.5 $$; Domain: $$ x \in R ; $$ Range: $$ y \geq 7.75 $$ Vertex: $$ (-3,9) $$; Axis of symmetry: $$ x=-1 $$;Domain: $$ x \in R ; $$ Range: $$ y \geq 9 $$

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To identify the vertex, axis of symmetry, domain, and range of a parabola, we need to understand the general properties of parabolas.

1. **Vertex**: The highest or lowest point of the parabola, depending on whether it opens upwards or downwards.
2. **Axis of Symmetry**: A vertical line that passes through the vertex, dividing the parabola into two mirror-image halves.
3. **Domain**: The set of all possible x-values for the parabola, which is typically all real numbers for parabolas.
4. **Range**: The set of all possible y-values, which depends on the vertex and the direction the parabola opens.

Now, let's analyze each option:

1. **Option 1**: 
   - Vertex: $$ (-1.5,-7.75) $$
   - Axis of symmetry: $$ x=-1.5 $$
   - Domain: $$ x \in R $$
   - Range: $$ y \geq -7.75 $$ (This is correct if the parabola opens upwards.)

2. **Option 2**: 
   - Vertex: $$ (-9,1) $$
   - Axis of symmetry: $$ x=-3 $$ (This is incorrect; the axis of symmetry should be the x-coordinate of the vertex.)
   - Domain: $$ x \in R $$
   - Range: $$ y \geq 1 $$ (This is correct if the parabola opens upwards.)

3. **Option 3**: 
   - Vertex: $$ (1.5,7.75) $$
   - Axis of symmetry: $$ x=1.5 $$
   - Domain: $$ x \in R $$
   - Range: $$ y \geq 7.75 $$ (This is correct if the parabola opens upwards.)

4. **Option 4**: 
   - Vertex: $$ (-3,9) $$
   - Axis of symmetry: $$ x=-1 $$ (This is incorrect; the axis of symmetry should be the x-coordinate of the vertex.)
   - Domain: $$ x \in R $$
   - Range: $$ y \geq 9 $$ (This is correct if the parabola opens upwards.)

Based on the analysis, the correct options are:

- **Option 1**: Vertex: $$ (-1.5,-7.75) $$; Axis of symmetry: $$ x=-1.5 $$; Domain: $$ x \in R $$; Range: $$ y \geq -7.75 $$
- **Option 3**: Vertex: $$ (1.5,7.75) $$; Axis of symmetry: $$ x=1.5 $$; Domain: $$ x \in R $$; Range: $$ y \geq 7.75 $$

However, Option 1 is the only one with a correct axis of symmetry. Therefore, the best choice is:

**Vertex: $$ (-1.5,-7.75) $$; Axis of symmetry: $$ x=-1.5 $$; Domain: $$ x \in R $$; Range: $$ y \geq -7.75 $$**.
The correct answer is: - **Vertex**: $$ (-1.5, -7.75) $$ - **Axis of Symmetry**: $$ x = -1.5 $$ - **Domain**: All real numbers ($$ x \in \mathbb{R} $$) - **Range**: $$ y \geq -7.75 $$

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