Find equation of parabola with focus and directrix

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To find the equation of a parabola with a focus at (0, -4) and a directrix of y = -2, the vertex is determined as the midpoint between these two points, which is (0, -3). The relationship D1 = D2, where D1 is the distance from the focus to any point on the graph and D2 is the distance from that point to the directrix, is crucial for deriving the equation. The resulting equation of the parabola is y + 3 = -1/4(x)^2. Understanding the vertex is essential for graphing the parabola accurately. This method effectively illustrates the geometric properties of parabolas.
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Homework Statement


Find the equation of the parabola with focus (0, -4) and directrix y = -2

i barely understand this thing. i mean how do i find the vertex.
the book says D1 = focus to any point on the graph, and D2= the point on the graph to the directrix. and D1 = D2. how do i graph if i don't know the vertex

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The Attempt at a Solution


answer: y + 3 = -1/4(x)2
 
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The vertex is the midpoint between the focus and the directrix.
 

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