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Re: calculate vertex of a parabola

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112791] Re: calculate vertex of a parabola
  • From: Murray Eisenberg <murray at math.umass.edu>
  • Date: Thu, 30 Sep 2010 04:53:44 -0400 (EDT)
  • Organization: Mathematics & Statistics, Univ. of Mass./Amherst
  • References: <i7sen7$ppb$1@smc.vnet.net> <201009290812.EAA27924@smc.vnet.net>
  • Reply-to: murray at math.umass.edu

Yes, of course when students are learning about completing the square, 
we want them to carry out the steps involved.

But once they have mastered it, to continue to insist they carry out 
those steps can become as pointless as to insist, for example, that they 
still extract square-roots using a paper-and-pencil algorithm.

On 9/29/2010 4:12 AM, Helen Read wrote:
> On 9/28/2010 6:06 AM, Murray Eisenberg wrote:
>> In his "Presentations" add-on application, David Park has a function
>> CompleteTheSquare that can save you the effort of carrying out the
>> manipulations:
>>
>>      <<Presentations`
>>
>>      CompleteTheSquare[a x^2 + b x + c, x] // InputForm
>> -b^2/(4*a) + c + a*(b/(2*a) + x)^2
>
>
> Personally, I'd like my students to understand how to do it the more
> effortful way :-)
>
> --
> Helen Read
> University of Vermont
>
>

-- 
Murray Eisenberg                     murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305


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