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Math Help - graphing problem

  1. #1
    Junior Member Godfather's Avatar
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    graphing problem

    If the graph of y=ax^2+bx+c passes through the points(-1,12),(0,5) and (2,-3) find the value of a+b+c
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Godfather View Post
    If the graph of y=ax^2+bx+c passes through the points(-1,12),(0,5) and (2,-3) find the value of a+b+c
    Here's how we go about it. We know that the y-intercept occurs when x is 0. And that in a polynomial of this form, the constant is the y-intercept. We see that one point is (0,5), that means when x is 0, y is 5, this implies c = 5. Now we use the other two points to obtain simultaneous equations.

    using (x,y) = (-1,12) we get

    a - b + 5 = 12..................................(1)

    using (x,y) = (2,-3) we get

    4a + 2b + 5 = -3...............................(2)

    Thus our equations are:

    a - b = 7...........................(1)
    4a + 2b = -8......................(2)

    So
    a - b = 7............................(1)
    2a + b = -4.........................(3) which we get by equation(2)/2

    Adding these equations we obtain
    3a = 3................................(1)+(3)
    so a = 1

    since a - b = 7
    => b = -6


    so the numbers are a = 1, b = -6 and c = 5
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