sketch and discuss the equation of the parabola 2x²+9y=0

The graph of the parabola \(y = -\frac{2}{9}x^2\) is shown above:

- **Vertex**: Located at the origin \((0, 0)\).
- **Focus**: At \((0, -\frac{9}{8})\), marked in green.
- **Directrix**: The horizontal line \(y = \frac{9}{8}\), marked with a dashed purple line.
- **Axis of Symmetry**: The \(y\)-axis.

The parabola opens **downward** due to the negative coefficient of \(x^2\). The graph visually confirms these properties.

Would you like more details or have any specific questions?

### Related Questions:
1. How do you find the vertex form of a parabola from its standard form?
2. How does the coefficient of \(x^2\) affect the width and direction of a parabola?
3. What are the equations for the focus and directrix of a parabola?
4. How do you find the x-intercepts and y-intercepts of a quadratic equation?
5. How can you determine the points where a parabola intersects a line?

**Tip:** Remember that the focus and directrix of a parabola are always equidistant from any point on the curve!

Explore and understand the equation of the parabola 2x² + 9y = 0 with detailed insights into its properties. This problem covers key concepts such as the standard form of a parabola, vertex form, focus, directrix, and axis of symmetry. Suitable for students in Grades 9-12.

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