How to write f ( x ) = x 2 + 4 x + 1 in vertex form?

Question

How to write             f              (        x        )              =          x      2        +    4    x    +    1   in vertex form?

Rhys Murphy · Accepted Answer

The equation in vertex form is             f              (        x        )              =    a                  (        x        -        h        )            2        +    k  Here, we have             f              (        x        )              =          x      2        +    4    x    +    1  , so we have       a    =    1  So for converting to this form, we complete the square using                     (        x        +        a        )            2        =          x      2        +    2    a    x    +          a      2       for which we have to identify       a   and then add and subtract             a      2       Thus,            f              (        x        )              =                            x          2                +        2        ×        2        ×        x        +                  2          2                    ̲        -          2      2        +    1        =                  (        x        +        2        )            2        -    4    +    1        =                  (        x        -                  (          -          2          )                )            2        -    3

How to write f ( x ) = x 2 + 4 x + 1...

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