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The quadratic $3x^2-24x+72$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. What is $a+b+c$

 Jul 11, 2020
 #1
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3 ( x^2-8x)         + 72     

                             'complete the square'    take 1/2 of the x coefficient square and add it ....and subtract it

3 (x^2-8x+16)      -48 + 72  

                                     (notice we had to subtract 3 times 16 because it is in the bracket multiplied by 3

3 (x-4)^2 +24    now you can add a b and c

 Jul 11, 2020

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