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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?

tertre  Mar 12, 2017
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re-arrange    -6x^2 + 36x =-216       Divide by -6  (we'll multiply by -6 shortly to even things out)

                        x^2 -6x =  36          'complete the square'

                        x^2 - 6x + 9 = 36+9

                        (x-3)^2 -45    now multiply by -6

 

                        -6(x-3)^2 + 270       a = -6   b = -3  c = 270

 

                    a+b+c = 261

ElectricPavlov  Mar 12, 2017
edited by ElectricPavlov  Mar 12, 2017

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