Find the general equation of the parabola with vertex at (3, 6) and focus at (3,4). Sketch the graph.

The graph of the parabola with vertex at \((3, 6)\) and focus at \((3, 4)\) is shown above. The parabola opens downward, with the vertex as the highest point. The directrix is the horizontal line \(y = 8\), and the axis of symmetry is the vertical line \(x = 3\).

Would you like to go over any details or have any questions about this? Here are some related questions for further exploration:

1. How would the equation change if the parabola opened upward?
2. What would be the equation of the directrix?
3. How can you find the length of the latus rectum?
4. How does the distance between the focus and vertex affect the shape of the parabola?
5. How would you write the equation if the parabola were shifted to a different vertex?

**Tip:** Remember, the sign of \(p\) determines the direction in which the parabola opens.

Explore the general equation of a parabola with a vertex at (3, 6) and a focus at (3, 4). Understand how the parabola opens downward, with detailed explanations of the vertex form, focus, directrix, and axis of symmetry. Suitable for advanced high school students.

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