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

Shadew  Dec 15, 2014

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 #1
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+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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3+0 Answers

 #1
avatar+92221 
+10
Best Answer

 

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

Melody  Dec 15, 2014
 #2
avatar+59 
+5

I'm confused. How did you get the -12x?

Shadew  Dec 16, 2014
 #3
avatar+92221 
+5

Hi shadew,

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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