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Q&A #12605

Teachers' Lounge Discussion: The geometry of the complex roots of graphs

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From: Doug Shields

To: Teacher2Teacher Public Discussion
Date: 2004040515:11:09
Subject: Algebraic expression of the vertex of the Phantom Parabola

I love the phantom parabola idea.  Here might be an addendum to that
day's lecture:

The vertex of the parabola corresponding to y = ax^2 + bx + c is at
(-b/2a, -b^2/4a + c).  

If the roots of the equation are complex, and we write the solutions
as r +/- si, then the coordinates of the vertex are simply (r, as^2).


Doug.

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