Here is the graph of the parabola with the focus at \((2, 2)\) and the directrix \(x = -8\). The key points and elements are:

- **Vertex**: \((-3, 2)\) (marked in red)
- **Focus**: \((2, 2)\) (marked in green)
- **Directrix**: \(x = -8\) (orange dashed line)

The equation of the parabola is \((y - 2)^2 = 20(x + 3)\).

Do you have any questions or need further details about this parabola?

### Follow-Up Questions

1. How do you determine the vertex of a parabola given the focus and directrix?
2. What is the significance of the directrix in a parabola?
3. How do you calculate the distance from the vertex to the focus?
4. Can you explain why the parabola opens to the right in this case?
5. What are the different forms of the parabola equations depending on their orientation?
6. How does the value of \(p\) affect the shape of the parabola?
7. How can you find the length of the latus rectum of this parabola?
8. How would the equation change if the directrix were horizontal?

### Tip

When graphing parabolas, always identify the vertex, focus, and directrix first. This helps in understanding the orientation and shape of the parabola.

Explore the graph of a parabola with focus at (2, 2) and directrix x = -8. Understand its key elements such as vertex, focus, and directrix, along with the equation (y - 2)^2 = 20(x + 3). Learn about parabola orientation and shape. Advanced high school level.

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