How to write the equation for a graph that is a parabola with a vertex at ( 5 , 3 ) ?

Question

How to write the equation for a graph that is a parabola with a vertex at             (      5      ,      3      )      ?

nebnikwjq · Accepted Answer

You can&#039;t find the equation for a parabola with just a vertex. You need another point.The equation for a parabola is       y    =    a                  (        x        -        h        )            2        +    k  You have       h    =    5   and       k    =    3   but no             (      x      ,      y      )       so then the equation becomes just       y    =    a                  (        x        -        5        )            2        +    3   which is not enough information to get the equation.There are no graphs with just one point. If all you have is a point, that&#039;s all it is.

Erica Lin · Accepted Answer

y    =    a          x      2        +    b    x    +    c        -          b              2        a              =    5                and              -          Δ              4        a              =    3        b    =    -    10    a                and              Δ    =    -    12    a    =    100          a      2        -    4    a    c    ⇒    c    =    25    a    +    3        y    =    a          x      2        -    10    a    x    +    25    a    +    3  Example:            x      2        -    10    x    +    28    =    0        Δ    =    100    -    4    ⋅    28    =    -    12  Therefore final answer:      x    =    5    ±    i          3

How to write the equation for a graph that is a parabola with a vertex at (5, 3)?

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