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Consider the function f(x)=x^2−6x−2 . Which equation shows function f written in vertex form? f(x)=(x−3)^2−5 ​ f(x)=(x+3)^2−11 ​ f(x)=(x+3)^2−5 ​ f(x)=(x−3)^2−11 ​

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MathPhys

Answer:

f(x) = (x − 3)² − 11

Step-by-step explanation:

To convert to vertex form, complete the square.

f(x) = x² − 6x − 2

f(x) = x² − 6x + 9 − 9 − 2

f(x) = (x − 3)² − 11

We need to complete the square: if we add and subtract 11 from the expression, we have

[tex]f(x)=x^2-6x-2=x^2-6x-2+11-11=x^2-6x+9-11=(x-3)^2+11[/tex]

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