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kmdb
 Post subject: Transformations
PostPosted: Thu, 5 Jul 2012 04:22:45 UTC 
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What would happen to its vertex?

2f(x), f(x)-3
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outermeasure
 Post subject: Re: Transformations
PostPosted: Thu, 5 Jul 2012 04:30:09 UTC 
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kmdb wrote:
What would happen to its vertex?

2f(x), f(x)-3


I see no vertices, so nothing happens. And I don't see any matrices either.

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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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Shadow
 Post subject: Re: Transformations
PostPosted: Thu, 5 Jul 2012 07:32:24 UTC 
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outermeasure wrote:
And I don't see any matrices either.


Agreed, topic moved to miscellaneous, until the op says more about what this problem deals with.

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Justin
 Post subject: Re: Transformations
PostPosted: Thu, 5 Jul 2012 15:28:25 UTC 
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kmdb wrote:
What would happen to its vertex?

2f(x), f(x)-3


It sounds like the OP is doing Algebra II...

If the vertex of f(x)=a(x-h)^2+k is (h, k), then

(i) 2f(x)=2a(x-h)^2+2k implies...
(ii) f(x)-3=a(x-h)^2+(k-3) implies...

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"Mathematicians are like lovers. Grant a mathematician the least principle, and he will draw from it a consequence which you must also grant him, and from this consequence another." Bernard Le Bovier Fontenelle (1657-1757)

"In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy."
G.H. Hardy (1877-1947)
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