Date: Fri, 16 Oct 1998 11:54:26 0600 (CST)
To: QandQ@MathCentral.uregina.ca
Sender: AGRrules@juno.com (Shay)
Subject: Parametrizing the left half of a parabola
Name: Shay
Who is asking: Student
Level: Secondary
Question:
Find the parametrized equation for the left half of the parabola with the equation: Y=x^24x+3
Hi Shay
y=x^24x+3 can be factored as y=(x1)(x3) so the vertex of the parabola is at x=2, midway between 1 and 3. To get the left side of the parabola you need to force the xcoordinate to be 2 or less. That is you want x to be 2 minus something that is positive, or at least 2 minus something that is never negative. Thus let x=2t^2 and whatever value t has, x will be less than or equal to 2. Now substitute x=2t^2 into y=x^24x+3 to find y in terms of t.
Cheers,
Chris
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