algebra

What is the equation, in standard form, of a parabola that models the values in the table?
x –2 0 4
ƒ(x) 1 5 -59

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  1. ax^2 + bx + c = 1
    plug in first value
    4a -2b + c = 1

    do the same for the others:

    0 + 0 + c = 5
    c = 5

    16a + 4b + c = -59

    so we plug in c into the equations with and b:

    16a + 4b + 5 = -59
    4a -2b + 5 = 1

    4a = 2b -4
    2a = b - 2

    16a + 4b = -64
    8(b-2) + 4b = -64

    2(b-2) + b = -16
    2b - 4 + b = -16
    3b = -12
    b = -4
    Plug in for a
    2a = -4 - 2
    2a = -6
    a = -3

    So the equation is:
    -3x^2 - 4x + 5

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