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.
Equation Graph Key Features Transformation

Answer 1

To best assist you, I’ll need a bit more context about the specific equations, graphs, key features, and transformations you have available. However, I can provide an example of how you might match these elements if you were given a set of common functions.

### Example:

**Equations:**
1. \( y = x^2 \)
2. \( y = (x - 3)^2 + 1 \)
3. \( y = -2(x + 1)^2 + 4 \)

**Graphs:** (You would usually present images of the graphs for these functions.)

**Key Features:**
- \( y = x^2 \):
- Vertex at (0,0)
- Opens upwards
- Symmetrical about the y-axis

- \( y = (x - 3)^2 + 1 \):
- Vertex at (3,1)
- Opens upwards
- Shifted right 3 units and up 1 unit from the parent function

- \( y = -2(x + 1)^2 + 4 \):
- Vertex at (-1,4)
- Opens downwards
- Reflected over the x-axis, vertically stretched by a factor of 2, and shifted left 1 unit and up 4 units

**Transformations:**
- Parent function \( y = x^2 \):
- No transformation
- Transformed to create \( y = (x - 3)^2 + 1 \):
- Right 3, Up 1
- Transformed to create \( y = -2(x + 1)^2 + 4 \):
- Left 1, Up 4, Reflect over x-axis, Vertically stretch by 2

### Matching Table:

| **Equation** | **Graph** | **Key Features** | **Transformation** |
|---------------------------------------------------|-------------------------|-------------------------------------------|-----------------------------------------------------|
| \( y = x^2 \) | (Graph of parabola) | Vertex at (0,0), Opens upwards | No transformation |
| \( y = (x - 3)^2 + 1 \) | (Graph of upward shift) | Vertex at (3,1), opens upwards | Right 3, Up 1 |
| \( y = -2(x + 1)^2 + 4 \) | (Graph of downward shift) | Vertex at (-1,4), opens downwards | Left 1, Up 4, Reflect over x-axis, Vertically stretch by 2 |

If you provide the specific functions and features you have, I can create a more tailored response!