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RE: [apcalculus] Going crazy
Posted:
Oct 15, 2012 9:40 PM


NOTE: This apcalculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus Teacher Community Forum at https://apcommunity.collegeboard.org/gettingstarted and post messages there.  I think the 'b' and the 'c' terms matter, too.
John Hanna jehanna@optonline.net www.johnhanna.us T3  Teachers Teaching with Technology "the future isn't what it used to be." Original Message From: John Losse [mailto:jlosse@me.com] Sent: Monday, October 15, 2012 4:14 PM To: AP Calculus Subject: RE:[apcalculus] Going crazy
NOTE: This apcalculus EDG will be closing in the next few weeks. Please sign up for the new AP Calculus Teacher Community Forum at https://apcommunity.collegeboard.org/gettingstarted and post messages there.   Did anyone notice that the intersection of the two tangent lines is the midpoint of the line segment joining the vertices of the parabolas? This leads to the following conjecture and an alternate way to approach the problem:
Conjecture: The graphs of two quadratic functions with leading coefficients which are "a" and "a" respectively, are symmetric with respect to the midpoint of their vertices.
A line through this midpoint which is tangent to one parabola will, by the symmetry, be tangent to the other.
The common tangents can therefore be found by the slightly different process of finding the tangents to a parabola from an external point.  To search the list archives for previous posts go to http://lyris.collegeboard.com/read/?forum=apcalculus
 To search the list archives for previous posts go to http://lyris.collegeboard.com/read/?forum=apcalculus



