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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 $c$ are constants. What is $a+b+c$?

 May 4, 2018

Best Answer 

 #1
avatar+20831 
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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 $c$ are constants.
What is $a+b+c$?

 

\(\begin{array}{|rcll|} \hline && -x^2+2x-4 \\ &=& -(x^2-2x)-4\\ &=& -\left((x-1)^2-1 \right) - 4 \\ &=& -(x-1)^2 +1 - 4 \\ &=& -(x-1)^2 -3 \quad & | \quad a(x+b)^2+c \\ &&& |\quad a=-1 \\ &&& |\quad b=-1 \\ &&& |\quad c=-3 \\ &&& |\mathbf{a+b+c} = -1-1-3 \mathbf{= - 5 } \\ \hline \end{array} \)

 

 

laugh

 May 4, 2018
 #1
avatar+20831 
+3
Best Answer

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

 

\(\begin{array}{|rcll|} \hline && -x^2+2x-4 \\ &=& -(x^2-2x)-4\\ &=& -\left((x-1)^2-1 \right) - 4 \\ &=& -(x-1)^2 +1 - 4 \\ &=& -(x-1)^2 -3 \quad & | \quad a(x+b)^2+c \\ &&& |\quad a=-1 \\ &&& |\quad b=-1 \\ &&& |\quad c=-3 \\ &&& |\mathbf{a+b+c} = -1-1-3 \mathbf{= - 5 } \\ \hline \end{array} \)

 

 

laugh

heureka May 4, 2018

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