Here are the graphs for the two parabolas based on the given conditions:

Case 1: Vertex (3, 2) and Focus (3, 0)

• Equation: $(x - 3)^2 = -8(y - 2)$
• Directrix: $y = 4$
• Length of Latus Rectum: 8
• Endpoints of Latus Rectum: (7, 0) and (-1, 0)
• Axis of Symmetry: $x = 3$

Case 2: Vertex (0, 2) and Focus (0, 5)

• Equation: $x^2 = 12(y - 2)$
• Directrix: $y = -1$
• Length of Latus Rectum: 12
• Endpoints of Latus Rectum: (6, 5) and (-6, 5)
• Axis of Symmetry: $x = 0$

Let me know if you need further clarification or additional details!

---

Here are 8 related questions you can explore:

1. What happens to the parabola if the directrix is moved closer to the vertex?
2. How does the focus determine the direction a parabola opens?
3. How do you find the vertex from the general equation of a parabola?
4. What is the significance of the latus rectum in determining the width of a parabola?
5. How do the equations of horizontal and vertical parabolas differ?
6. How do changes in $p$ (distance to focus) affect the shape of a parabola?
7. How can you determine the equation of the axis of symmetry from the equation of the parabola?
8. What are some real-world applications of parabolas?

Tip: The distance between the focus and the vertex, $p$, controls how "wide" or "narrow" the parabola is. A larger $|p|$ results in a wider parabola.