SOLUTION: Step by step, how do I write the standard form equation of a parabola with vertex at(0,0) and a focus of (0,-3)?

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Question 747205: Step by step, how do I write the standard form equation of a parabola with vertex at(0,0) and a focus of (0,-3)?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
1) vertex (0,0)=(h,k) and focus (0,3)=(h,k+a)
standard equation: if vertex and focus have same x coordinate, equation is
%28x-h%29%5E2=4a%28y-k%29
so, your equation is:
%28x-0%29%5E2=4a%28y-0%29
x%5E2=4ay........since (0,3)=(h,k+a) => k%2Ba=3=> 0%2Ba=3 => a=3
x%5E2=4%2A3y
x%5E2=12y
y=%281%2F12%29x%5E2