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Given that the zeros of a quadratic function are –2 and 8, what is the standard form of the quadratic function?

Given that the zeros of a quadratic function are –2 and 8, what is the standard form of the quadratic function?
A f(x) = x² + 6x + 16
B f(x) = x² + 6x – 16
C f(x) = x² – 6x + 16
D f(x) = x² – 6x – 16




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1 Answer

  1. To find the standard form of a quadratic function given its zeros, we can use the factored form of the quadratic function. If the zeros are ( r_1 ) and ( r_2 ), the quadratic function can be expressed as:

    [ f(x) = a(x – r_1)(x – r_2) ]

    Given the zeros are –2 and 8, we can plug these values in:

    [ f(x) = a(x + 2)(x – 8) ]

    Now let’s expand this:

    1. First, expand the factors:

    [

    f(x) = a[(x + 2)(x – 8)] = a(x^2 – 8x + 2x – 16) = a(x^2 – 6x – 16)

    ]

    2. By setting ( a = 1 ) (for the standard form), we get:

    [

    f(x) = x^2 – 6x – 16

    ]

    So the standard form of the quadratic function is:

    D ( f(x) = x^2 – 6x – 16 )

    This choice matches the expanded expression, confirming it’s correct.

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