SOLUTION: Please write an equation given vertex (-2,3) focus (-2, 8)

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Question 1010589: Please write an equation given vertex (-2,3) focus (-2, 8)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Using the formula and avoiding the process of deriving the equation, %28x-h%29%5E2=4p%28y-k%29 for the basic formula. Vertex as given means h=-2 and k=3; the focus is 8-3=5 units above the vertex, so you know that the directrix is 5 units below the vertex, being there as y=3-5=-2.

Vertex and focus orientation indicate 4p is POSITIVE, the parabola opening UPWARD, vertex a minimum.

4p=4%2A5
4p=20

and plugging in coordinates for the vertex,
highlight%28%28x-%28-2%29%29%5E2=20%28y-3%29%29.
From here, adjust the form any way you need.