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17 June, 22:26

If you use the zeros, you can write the factored form of p (x) as p (x) = (x + 3/4) (x - 4/3) * (x - 2/5) than as p (x) = (4x + 3) (3x - 4) * (5x - 2). What is the relationship of the factors between two forms? Give this relationship in general form.

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  1. 17 June, 22:36
    0
    Answer: The standard form for the equation of an ellipse is:

    (

    x

    -

    h

    )

    2

    a

    2

    +

    (

    y

    -

    k

    )

    2

    b

    2

    =

    1

    The center is:

    (

    h

    ,

    k

    )

    The vertices on the major axis are:

    (

    h

    -

    a

    ,

    k

    )

    and

    (

    h

    +

    a

    ,

    k

    )

    The vertices on the minor axis are:

    (

    h

    ,

    k

    -

    b

    )

    and

    (

    h

    ,

    k

    +

    b

    )

    The foci are:

    (

    h

    -



    a

    2

    -

    b

    2

    ,

    k

    )

    and

    (

    h

    +



    a

    2

    -

    b

    2

    ,

    k

    )

    To put the given equation in standard form, change the + 2 to - - 2 and write the denominators as squares:

    (

    x

    -

    3

    )

    2

    4

    2

    +

    (

    y

    -

    -

    2

    )

    2

    3

    2

    =

    1

    The center is:

    (

    3

    ,

    -

    2

    )

    The vertices on the major axis are:

    (

    -

    1

    ,

    -

    2

    )

    and

    (

    7

    ,

    -

    2

    )

    The vertices on the minor axis are:

    (

    3

    ,

    -

    5

    )

    and

    (

    3

    ,

    1

    )

    Evaluate:



    a

    2

    -

    b

    2

    =



    4

    2

    -

    3

    2

    =



    16

    -

    9

    =



    5

    The foci are:

    (

    3

    -



    5

    ,

    -

    2

    )

    and

    (

    3

    +



    5

    ,

    -

    2

    )
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