How do I find the vertex of f ( x ) = x 2 + 6 x + 5 ?

Question

How do I find the vertex of             f              (        x        )              =          x      2        +    6    x    +    5  ?

Hunter Hendricks · Accepted Answer

given the parabola in                             standard form                  •                  x              y    =    a          x      2        +    b    x    +    c                  x              ;    a    ≠    0              then the x-coordinate of the vertex is            •                  x                    x                                    vertex                                =    -          b              2        a                        f              (        x        )              =          x      2        +    6    x    +    5                 is in standard form                  with               a    =    1    ,    b    =    6                 and               c    =    5              x                        vertex                      =    -          6      2        =    -    3              substitute this value into the equation for y                  y                        vertex                      =                  (        -        3        )            2        +    6          (      -      3      )        +    5    =    -    4        ⇒                  vertex                       =          (      -      3      ,      -      4      )       graph{x^2+6x+5 [-10, 10, -5, 5]}

Kiara Rollins · Accepted Answer

The given function:            f              (        x        )              =          x      2        +    6    x    +    5        y    =          x      2        +    2          (      3      )        x    +          3      2        -          3      2        +    5        y    =                  (        x        +        3        )            2        -    4                      (        x        +        3        )            2        =          (      y      +      4      )      The following equation is a vertical parabola in its standard form:                     (        x        -                  x          1                )            2        =    4    a          (      y      -              y        1            )      Which has vertex at             (              x        1            ,              y        1            )        ≡          (      -      3      ,      -      4      )

How do I find the vertex of f ( x ) = x 2 +...

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