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Here is the graph of the parabola based on the equation \( (y-2)^2 = 8(x+1) \). The red 'X' marks the vertex at (-1,2), and the green mark indicates the focus at (1,2), which is 2 meters to the right of the vertex. The dotted line represents the axis of symmetry, \( y = 2 \).

Do you have any further questions or need more details on this? Here are some follow-up queries you might consider:

1. How do you find the directrix of this parabola?
2. What is the significance of the focus in parabolic antennas?
3. How does the orientation of the parabola affect its properties?
4. Can you explain the derivation of the vertex form equation for a parabola?
5. How would you adjust the equation if the parabola were to open in a different direction?

**Tip:** When solving real-world problems involving parabolas, like this satellite dish example, it's crucial to understand the role of the focus and directrix to optimize the function of the device.

The interior of a satellite TV antenna is a dish having the shape of a paraboloid. Its receiver is placed 2 meters from the vertex. If the vertex is at (-1,2) and it opens to the right, find the equation (in general form) of the parabola, and graph it completely.

Learn how to find the equation of a parabola for a satellite dish antenna with a vertex at (-1, 2) and its receiver 2 meters to the right. This problem covers key geometry concepts such as the equation of a parabola and its focus.

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