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Topic: 2 parabolas from 1 Function
Replies: 1   Last Post: Aug 3, 2007 10:21 AM

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 R. Brown Posts: 54 From: texas Registered: 12/29/05
2 parabolas from 1 Function
Posted: Jul 13, 2007 10:57 AM

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

Date Subject Author
7/13/07 R. Brown
8/3/07 R. Brown