How to Find the vertex, Focus, and directrix of the Parabola and sketch its graph ( x - 3 ) + ( y - 2 ) 2 = 0 ?

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How to Find the vertex, Focus, and directrix of the Parabola and sketch its graph             (      x      -      3      )        +                  (        y        -        2        )            2        =    0  ?

sarabol2zsr · Accepted Answer

the equation of a horizontally opening parabola is            •                  x                            (        y        -        k        )            2        =    4    a          (      x      -      h      )                  where                     (      h      ,      k      )                     are the coordinates of the vertex and a is                  the distance from the vertex to the focus and directrix                  If               a    &amp;gt;    0                 opens to the right                         If               a    &amp;lt;    0                 opens to the left                  rearrange the given equation into this form                          (        y        -        2        )            2        =    -          (      x      -      3      )                  with vertex               =          (      3      ,      2      )            4    a    =    -    1    ⇒    a    =    -          1      4                     so opens to the left                  Focus               =          (      a      +      h      ,      k      )        =          (      -              1        4            +      3      ,      2      )        =          (              11        4            ,      2      )                  directrix is               x    =    -    a    +    h    =          1      4        +    3    =          13      4                  for x-intercept let y = 0            4    =    -    x    +    3    ⇒    x    =    -    1              for y-intercepts let x = 0                          (        y        -        2        )            2        =    3    ⇒          (      y      -      2      )        =    ±          3            y    =    2    ±          3            y    ≈    3.73    ,    y    ≈    0.27              Plot the above coordinates for vertex, focus and                         intercepts and draw a smooth curve through them       graph{(y-2)^2=-(x-3) [-10, 10, -5, 5]}

How to Find the vertex, Focus, and directrix of the Parabola and sketch its graph (x-3)+(y-2)^2=0?

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