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The quadratic \(-6x^2+36x+216\) can be written in the form \(a(x+b)^2+c\), where a, b, and c are constants. What is a+b+c?

 Aug 27, 2018
 #1
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First factor out a -6 to get \(-6(x^2-6x-36)\)

Then complete the square to get \(-6(x^2-6x+9)+270 ​​\) because 216+54=270

This simplifies to \(-6(x-3)^2+270\)

So \(a=-6\)\(b=-3\), and \(c=270\)  and \(a+b+c=-6+(-3)+270=261\)

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 Aug 27, 2018

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