Re: Twin Parabola Puzzle/Conjecture

On Sep 4, 6:55 pm, col.r...@xxxxxxxxxxxxxx wrote:
Ok, it may be trivial to note that the 'linear function' was created
by limiting the domain of the independent variable (y) so that there
are only 2 possible values for (x)....... Namely: x' and x"

y' = a (x')^2 + b x' + c

y" = a (x")^2 + b x" + c

Since:
y'= 0
and:
y"= 0

y'= y"

Ok, let's now assume that in the above problem, the constants are:

a= .5
b= .7071067
c= -.25

vertex y= -.5
vertex x= -.7071067

Now, the question becomes "Can you write a 'general quadratic
function' that will incorporate all of the 'points' in the above
parabola and ALSO include a 2nd parabola which will intersect this
parabola, at it's vertex?"

If you can do this, you have solved the Twin Parabola Puzzle.
Compliments of Col. Rbtx, the Barnyard Physicist of Texas

Not clear what you exactly want. This 3D Hypar is too well-known.
http://mathworld.wolfram.com/HyperbolicParaboloid.html

.

Relevant Pages

  • Re: Twin Parabola Puzzle/Conjecture
    ... it may be trivial to note that the 'linear function' was created ... by limiting the domain of the independent variable so that there ... parabola and ALSO include a 2nd parabola which will intersect this ... you have solved the Twin Parabola Puzzle. ...
    (sci.math)
  • Re: Twin Parabola Puzzle/Conjecture
    ... by limiting the domain of the independent variable so that there ... function' that will incorporate all of the 'points' in the above ... parabola and ALSO include a 2nd parabola which will intersect this ...
    (sci.math)
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