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The quadratic -x^2 + 12x - 4 can be written in the form a(x + b)^2 + c, where a, b, and c are constants. What is a+b+c?

Dec 11, 2020

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The quadratic -x^2 + 12x - 4 can be written in the form a(x + b)^2 + c, where a, b, and c are constants. What is a+b+c?

Hello Guest!

\(\color{BrickRed} -x^2 + 12x - 4\\ =a(x+b)^2+c\\ =a(x^2+2bx+b^2)+c\\ \color{BrickRed}=ax^2+2abx+ab^2+c\)

\(\color{blue}a=-1\\ 2ab=12\\ ab^2+c=-4\)

\(-2b=12\\ \color{blue}b=-6\)

\((-1)(-6)^2+c=-4\\ c=-4+36\)

\(c=32\color{blue}\)

\(a+b+c=(-1)+(-6)+(32)=25\)

!

Dec 12, 2020
edited by asinus  Dec 12, 2020