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Nana76 [90]
2 years ago
9

Rewrite the function by completing the square (vertex form) f(x)=x^2+16x-46

Mathematics
1 answer:
insens350 [35]2 years ago
5 0

Answer:

\large\boxed{f(x)=(x+8)^2-110}

Step-by-step explanation:

\text{The vertex form of equation}\ y=ax^2+bx+c:\\\\y=a(x-h)^2+k\\\\\text{We have the equation:}\\f(x)=x^2+16x-46=x^2+2(x)(8)-46=x^2+2(x)(8)+8^2-8^2-46\\\\\text{use}\ (a+b)^2=a^2+2ab+b^2\to x^2+2(x)(8)+8^2=(x+8)^2\\\\f(x)=(x+8)^2-64-46=(x+8)^2-110

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