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April 23rd, 2012, 04:19 AM  #1 
Member Joined: Nov 2011 Posts: 45 Thanks: 0  equation of a split parabola
what is the equation that gives a curve (similar x² = y) but with half curve in the first and half in the third quadrant? If that is not clear : I mean a curve, a function, similar (mutatis mutandis) to x³ = y Thanks 
April 23rd, 2012, 08:41 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: equation of a split parabola
You could use: 
April 24th, 2012, 04:36 AM  #3  
Member Joined: Nov 2011 Posts: 45 Thanks: 0  Re: equation of a split parabola Quote:
This equation has 3 real roots, right? how do we find them?  
April 24th, 2012, 04:52 AM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: equation of a split parabola
According to the computer, that equation has no real roots.

April 24th, 2012, 09:08 PM  #5  
Member Joined: Nov 2011 Posts: 45 Thanks: 0  Re: equation of a split parabola Quote:
consider also: xx  5x =4, can you find the 3 roots? For all y beween the extrema (+,6.25) you get 3 real roots. How do you find them? Thanks  
April 24th, 2012, 09:45 PM  #6  
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: equation of a split parabola Quote:
Quote:
Case 1: From this you find two real roots if k is nonpositive (repeated if k is on the boundary). If k is negative you get 1 real root. Case 2: If k is nonpositive, you get 1 real negative root, and you discard the positive root. If k is positive, you get 2 real negative roots.  
April 25th, 2012, 03:13 AM  #7  
Member Joined: Nov 2011 Posts: 45 Thanks: 0  Re: equation of a split parabola Quote:
consider : xx  5x =+,(makes no difference the value doew not change) 3, how do you find the 3 roots?  
April 25th, 2012, 08:12 AM  #8 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs  Re: equation of a split parabola
There is no formula, you essentially have a piecewise defined function, and you have to consider each piece as a separate case.

April 25th, 2012, 08:19 AM  #9  
Member Joined: Nov 2011 Posts: 45 Thanks: 0  Re: equation of a split parabola Quote:
 
April 25th, 2012, 11:26 PM  #10  
Member Joined: Nov 2011 Posts: 45 Thanks: 0  Re: equation of a split parabola Quote:
Try it a wolfram and you'll find the 3 real solutions.  

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