Find an equation of a parabola with a vertex at the origin and directrix y = –2.5
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The equation of the parabola is:

Step-by-step explanation:

Since the directrix is the line y = -2.5, this is a horizontal line ; thus the parabola opens up or down.

, where (h, k) is the vertex, the focus is (h, k + p), and the directrix is y = k - p.

The vertex is (h, k), or (0,0)

The directrix is y = -2.5

so k - p = -2.5

⇒    0 - p = -2.5

⇒ p = 2.5

The focus is (h, k + p)

⇒ (0, 0 +2.5)=(0, 2.5)

Thus substituting the values into the base equation,

Hence the equation of the parabola is:

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