If f (x) = x^2 − 2x , show by completing the square that; f (x − 1) = (x − 2)^2 − 1.

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jeew-m | College Teacher | (Level 1) Educator Emeritus

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`f(x) = x^2-2x`

To get `f(x-1)` we should replace `x` by `(x-1)` .

`f(x-1) = (x-1)^2-2(x-1)`

`f(x-1) = x^2-2x+1-2x+2`

`f(x-1) = x^2-4x+3`

`x^2-4x`

`= x^2-4x+4-4`

`= (x^2-4x+4)-4`

`= (x-2)^2-4`

`f(x-1) = (x-2)^2-4+3`

`f(x-1) = (x-2)^2-1`

So the required answer is obtained.

`f(x-1) = (x-2)^2-1`

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