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15 July, 11:32

Apply your knowledge of factoring and zero product property to write a quadratic function when given - 2 and 2/3 as the zeros. (Show all work for full credit)

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  1. 15 July, 12:37
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    When the zeros are - 2 and 2/3

    The factors of the equation would be (x + 2) and (x-2/3)

    Now you have (x+2) (x-2/3) = 0

    Now expand using FOIL:

    xx + x (-2/3) + 2x+2 (-2/3) = 0

    Simplify ad combine like terms:

    x^2 * 3 + (-2x+2x*3) - 4 / 3 = 0

    Simplify the numerator:

    (3x-2) (x+2) / 3 = 0

    Expand the numerator using FOIL:

    3xx + 3x*2-2x-2*2 / 3 = 0

    Simplify and combine like terms:

    3x^2 + 4x-4 / 3 = 0

    Splpit into 3 fractions:

    3x^2 / 3 + 4x/3 + - 4/3 = 0

    Cancel common factors:

    x^2 + 4x/3 - 4/3 = 0

    The quadratic formula is:

    y = x^2 + 4x/3 - 4/3
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