The equation \( x^2 = -6y \) represents a **parabola** that opens **downward** along the **y-axis**. 

### Key Features:
1. **Vertex**: The vertex of the parabola is at the origin \((0,0)\).
2. **Direction**: The negative sign in front of \(6y\) means the parabola opens downward.
3. **Axis of Symmetry**: The axis of symmetry is the y-axis (\(x = 0\)).
4. **Standard Form**: The equation is similar to the standard form of a parabola \(x^2 = 4py\), where \(p\) is the distance from the vertex to the focus. In this case, \(4p = -6\), so \(p = -\frac{3}{2}\), meaning the focus is 1.5 units below the vertex at \((0, -1.5)\).

### Conclusion:
- The parabola opens downward with a vertex at the origin, and its focus lies below the vertex by 1.5 units.

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Here are 5 related questions:
1. How do you convert this equation to the general form of a parabola?
2. What are the focus and directrix of this parabola?
3. How would the graph change if the equation were \(x^2 = 6y\)?
4. How do you find the focal length from this equation?
5. What is the axis of symmetry for other parabolas of the form \(x^2 = ay\)?

**Tip**: Parabolas are symmetric along their axis, making it easy to find points on one side and mirror them on the other.

Explore the properties of the parabola equation x^2 = -6y, which represents a parabola opening downward with its vertex at the origin. Learn about the focus, axis of symmetry, and key formulas used to solve this geometry problem. Suitable for students in Grades 10-12.

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