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The quadratic -6x^2+72x+216 can be written in the form a(x+b)^2+c, where a, b, and c are constants. What is a+b+c?

 Dec 3, 2020
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-6x^2  + 72x  +  216  ...... factor  out the  -6

 

-6 ( x^2  - 12x   - 36)

 

Take 1/2 of 12  = 6....square it  = 36......add and subtract it within the parentheses

 

-6 ( x^2   - 12x  + 36   - 36   -36  )       factor the  first three terms and simplify the rest

 

-6 [ ( x  - 6)^2   -  72  ]        distribute the  -6 across  the terms in the brackets

 

-6(x - 6)^2   +  252

 

a =  -6      b  =  -6      c =   252

 

And their sum  =  240

 

cool cool cool

 Dec 3, 2020

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