Question

The parent function is f(x) = x^2.
The value of k is 4.

On
 a graph, put down y = f(x) and y = f(x) +/= k for your
 parent function and chosen value of k. Be sure to clearly label each sketch.

Answer 1

Sure! To understand the transformations of the parent function \( f(x) = x^2 \) when we add or subtract a constant \( k \), we can analyze the following equations:

1. The parent function:
\[
y = f(x) = x^2
\]

2. The transformed function with \( k = 4 \):
\[
y = f(x) + k = x^2 + 4
\]

3. For subtraction, it would be:
\[
y = f(x) - k = x^2 - 4
\]

### Graphing Instructions

1. **Parent Function \( y = x^2 \)**:
- This is a standard upward-opening parabola with its vertex at the origin (0,0).
- Important points to plot:
- (0,0)
- (-1, 1)
- (1, 1)
- (-2, 4)
- (2, 4)

2. **Transformed Function \( y = x^2 + 4 \)**:
- This graph is also a parabola that opens upwards but is shifted **up** by 4 units.
- Important points to plot:
- (0, 4)
- (-1, 5)
- (1, 5)
- (-2, 6)
- (2, 6)

3. **Transformed Function \( y = x^2 - 4 \)**:
- This graph is again a parabola that opens upwards but is shifted **down** by 4 units.
- Important points to plot:
- (0, -4)
- (-1, -3)
- (1, -3)
- (-2, 0)
- (2, 0)

### Visual Representation

Here's a description of how to sketch it:

- **Sketch the Parent Function**:
- Draw a parabola opening upwards, passing through the origin and plotting the points mentioned above.

- **Sketch \( y = x^2 + 4 \)**:
- Draw another upward-opening parabola parallel to the first, shifted 4 units upwards. Make sure to label this graph as \( y = x^2 + 4 \).

- **Sketch \( y = x^2 - 4 \)**:
- Similarly, draw yet another upward-opening parabola parallel to the first but shifted 4 units downwards. Label this graph as \( y = x^2 - 4 \).

### Labeling

Be sure to include labels next to each curve:
- For the parent function: "y = x^2"
- For the transformed function up: "y = x^2 + 4"
- For the transformed function down: "y = x^2 - 4"

### Conclusion

You now have a clear visual representation of the parent function and its transformations by vertically shifting it up or down by 4 units. If you choose to draw or use graphing software, it will reinforce the concepts of transformations in a quadratic function.