Find real numbers a, b, and c such that the graph of the function y = ax2 + bx + c contains the points (1, 2), (2, 11), and (-3, -14). 1)?

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  • TomV
    Lv 7
    1 year ago
    Favorite Answer

    y = ax² + bx + c

    eq1: a + b + c = 2

    eq2: 4a + 2b + c = 11

    eq3: 9a - 3b + c = -14

    From eq1, c = 2-a-b

    Substitute into eq2 and eq3

    4a + 2b + 2 - a - b = 11

    9a - 3b + 2 - a - b = -14

    Collect like terms:

    eq4: 3a + b = 9

    eq5: 8a - 4b = -16

    From eq4: b = 9-3a

    Substitute into eq5 and collect like terms

    8a - 4(9-3a) = -16

    8a + 12a = 20

    20a = 20

    a = 1

    b = 9-3a = 9-3 = 6

    c = 2-1-6 = -5

    Ans: (a, b, c) = (1, 6, -5)

    =======================

    Check:

    f(x) = y = x² + 6x - 5

    f(1) = 1+6-5 = 7-5 = 2 : True

    f(2) = 4 + 12 - 5 = 16-5 = 11 : True

    f(-3) = 9 - 18 - 5 = 4 - 18 = -14 : True

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