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R. Brown
Posts:
54
From:
texas
Registered:
12/29/05
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2 parabolas from 1 Function
Posted:
Jul 13, 2007 10:57 AM
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I proposed some months ago that it might be possible to state a function, in which 2 parabolas would be the result of one function. I know present the following as the most concise way this can be done. Consider:
F(y)= {x + zi | A(x + zi)^2 + B(x + zi) + C = y }
Now I state the 'domain' of the independent variable:
-[inf]< y < [inf]
Then:
If the 'extended discriminant' = B^2 - 4A(C-y)
When the extended discriminant is greater than zero:
z= 0 ===> zi= 0
When the extended discriminant is less than zero:
zi =/= 0 .....===>
x= -B/2A
I predict that the result of the above function will be 2 parabolas in 3-dimensional space that intersect at the vertex(s).
Original Math/Compliments of Robt W. Brown/Barnyard Physicist of Texas
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