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Topic: [ap-calculus] Going crazy
Replies: 2   Last Post: Oct 17, 2012 1:48 PM

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John Hanna

Posts: 106
Registered: 1/8/11
RE: [ap-calculus] Going crazy
Posted: Oct 15, 2012 9:40 PM
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NOTE:
This ap-calculus 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/getting-started
and post messages there.
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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:[ap-calculus] Going crazy

NOTE:
This ap-calculus 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/getting-started
and post messages there.
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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.
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