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The quadratic  \(-x^2+2x-4\)can be written in the form \(a(x+b)^2+c\), where a, b, and b are constants. What is a+b+c?

 Aug 6, 2018
 #1
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-x^2 + 2x - 4       let us complete the square....factor out a "-1"  and we have

 

- ( x^2 - 2x  + 4)        take 1/2 of -2  = -1, square it  = 1...add and subtract it inside the parentheses

 

- ( x^2 - 2x + 1  + 4  - 1)       factor the first three terms, simplify the rest

 

- [ ( x - 1)^2   + 3 )       apply the ngative back across the terms

 

- ( x - 1)^2  -3 

 

"a"  = -1

"b"  = -1

"c"  = -3

 

So

 

a + b + c  =    -1  +  -1  + -3  =   -5

 

 

cool cool cool

 Aug 7, 2018

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