graph this: vertex (0,0), focus(-5/4), diretrix(x=5/4), a of s(y=0), lr1(-5/4,5/2), lr2(-5/4,-5/2)

Here is the graph of the parabola \( y^2 = -5x \) based on the provided information:

- The vertex is at \((0, 0)\).
- The focus is at \(\left(-\frac{5}{4}, 0\right)\), marked in red.
- The directrix is the green dashed line at \(x = \frac{5}{4}\).
- The latus rectum endpoints are at \(\left(-\frac{5}{4}, \frac{5}{2}\right)\) and \(\left(-\frac{5}{4}, -\frac{5}{2}\right)\), marked in magenta.

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. How would the graph change if the focus were at \(\left(\frac{5}{4}, 0\right)\)?
2. What is the relationship between the distance from the focus and the directrix to any point on the parabola?
3. How would you find the equation of a parabola given the vertex and the directrix?
4. What would be the equation of the parabola if the vertex were at \((2, -1)\)?
5. How can you derive the equation of the latus rectum?

**Tip:** The directrix and the focus always maintain equal distance from any point on the parabola, making it a useful method for constructing parabolas geometrically.

Explore the graph of the parabola y^2 = -5x with detailed annotations for the vertex, focus, directrix, and latus rectum endpoints. Understand the geometric properties and relationships of key elements in this conic section. Suitable for high school students studying parabolas and conic sections.

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