Question

Match the equation, graph, key features, and the transformation on the parent function to the table of values of each function.

(5 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
x y
-2 -12
-1 -6
0 0
1 -6
2 -12

Equation Graph Key Features Transformation

Answer 1

Based on the provided table of values, let’s begin by analyzing the relationship between \(x\) and \(y\).

The given values are:
- When \(x = -2\), \(y = -12\)
- When \(x = -1\), \(y = -6\)
- When \(x = 0\), \(y = 0\) (which suggests this could be a transformation affecting the graph)
- When \(x = 1\), \(y = -6\)
- When \(x = 2\), \(y = -12\)

This table of values suggests a quadratic function because the values for \(y\) have a symmetrical pattern. Upon inspecting the graph, the function appears to be a downward-opening parabola.

### Table of Inputs:
1. **Equation**: The quadratic function can be represented as:
\[
y = -3(x^2 - 1) = -3x^2 + 3
\]
Although it can also take other forms based on the vertex. However, from the y-values we conclude that the equation is in the form of:
\[
y = -3(x^2)
\]

2. **Graph**: This would show a parabola opening downwards, having its vertex at \((0, 0)\) and symmetric about the y-axis.

3. **Key Features**:
- The vertex at \((0, 0)\)
- The function is symmetric about the y-axis
- It opens downwards
- The maximum point is at the vertex, which is 0

4. **Transformation**: There is a vertical stretch by a factor of 3 and a reflection across the x-axis.

### Final Reflections and Summary:
- **Equation**: \( y = -3(x^2) \)
- **Graph**: Downward-opening parabola
- **Key Features**: Vertex at \((0, 0)\), symmetric, opens downwards
- **Transformation**: Vertical stretch (by factor 3) and reflection across the x-axis

So, you can input your final answers as follows:

**Equation**: \( y = -3(x^2) \)
**Graph**: (Illustration of a downward-opening parabola)
**Key Features**: "Vertex at (0, 0), symmetric, opens downwards"
**Transformation**: "Vertical stretch (by factor 3) and reflection across the x-axis"

In practice, the exact presentation will depend on the specific requirement of your assignment or worksheet structure.