An arch in a memorial park, having a parabolic shape, has a base width of 28 feet and opens downward
with the vertex at the origin. Suppose the base serves as its latus rectum. Find the equation (in standard
form) that models this shape, then graph it. State the focus, directrix, and axis of symmetry.

Here is the graph of the parabola \( x^2 = -28y \).

### Summary:
- **Equation of the Parabola**: \( x^2 = -28y \)
- **Focus**: \( (0, -7) \)
- **Directrix**: \( y = 7 \)
- **Axis of Symmetry**: \( x = 0 \) (the y-axis)

The graph shows the parabola opening downward, with the focus and directrix properly positioned relative to the vertex.

Do you want more details or have any questions? Here are some related questions:

1. What would be the equation if the parabola opened upwards?
2. How does the equation change if the vertex is not at the origin?
3. What is the significance of the latus rectum in a parabola?
4. Can you find the length of the parabola's chord parallel to the latus rectum?
5. How would the equation change if the parabola were stretched horizontally?

**Tip**: When solving problems involving parabolas, always identify the vertex, focus, and directrix first to establish the correct form of the equation.

Explore the mathematical modeling of a parabolic arch in a memorial park, with a base width of 28 feet and the vertex at the origin. Learn the equation of the parabola, its focus, directrix, and axis of symmetry, and visualize its graph. Suitable for high school students studying coordinate geometry and quadratic equations.

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