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Standard Form conversion

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How would I convert this equation to standard form? y = -2 (x - 6)^2 + 8

#1
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$$\\y = -2 (x - 6)^2 + 8\\ y=-2(x^2-12x+36)+8\\ y=-2x^2+24x-72+8\\ y=-2x^2+24x-64\\$$

Melody  Dec 15, 2014
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#1
+92221
+10

$$\\y = -2 (x - 6)^2 + 8\\ y=-2(x^2-12x+36)+8\\ y=-2x^2+24x-72+8\\ y=-2x^2+24x-64\\$$

Melody  Dec 15, 2014
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I'm confused. How did you get the -12x?

#3
+92221
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Sorry I took so long to get back to you I have been busy today.

I am very glad that you asked - I like to get feed back :)

This is the long way I could have done     $$(x-6)^2$$

$$\\(x-6)^2\\ =(x-6)(x-6)\\ =x(x-6)\;\;-6(x+6)\\ =x^2-6x\;\;-6x-36\\ =x^2-12x+36$$

Now $$(x-6)^2$$     is a perfect square.   There is a short cut method.

$$\\(a\pm b)^2=a^2\;\pm\;(2*a*b)\;+\;b^2\\ so\\ (x-6)^2=x^2\;-\;(2*x*6)\;+\;6^2=x^2-12x+36$$

I sometimes use this method when I want to square numbers in my head

eg

$$\\23^2\\ =(20+3)^2\\ =20^2+(2*20*3)+3^2\\ =400+120+9\\ =529$$

Melody  Dec 16, 2014

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