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Math Help - Find expressions for the quadratic functions whose graphs are shown.

  1. #1
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    Find expressions for the quadratic functions whose graphs are shown.

    Find expressions for the quadratic functions whose graphs are shown.



    I know how to do f(x) but I'm stuck on g(x).
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  2. #2
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    Quote Originally Posted by zweevu View Post
    Find expressions for the quadratic functions whose graphs are shown.



    I know how to do f(x) but I'm stuck on g(x).
    First, note that the y-intercept is 1.

    So g(x) = ax^2 + bx + 1.


    Using the other two points, we will have two equations in two unknowns to solve simultanously.

    Equation 1:
    2 = a(-2)^2 + b(-2) + 1

    4a - 2b + 1 = 2

    4a - 2b = 1.


    Equation 2:
    -2.5 = a(1)^2 + b(1) + 1

    a + b + 1 = -2.5

    a + b = -1.5.


    So your system of equations is...

    4a - 2b = 1

    a + b = -1.5.


    Solve for a and b.
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  3. #3
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    The second function has the form

     y = ax^2+bx+c

    The y-intercept c is 1 as shown in the picture so

     y = ax^2+bx+1

    Now use points (-2,2)

     y = ax^2+bx+1

     2 = a(-2)^2+b(-2)+1 ...(1)

    and (1,-2.5)

     y = ax^2+bx+1

     -2.5 = a(1)^2+b(1)+1 ...(2)

    and solve the sytem
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  4. #4
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    The question is looking g(x) = ... what would I type in for the answer. I got +/- 1/6 for a and b though.

    Edit: NVM You plug them into the original equation. Thanks!
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    You have g(x) = y = ax^2+bx+c

    With c = 1 , b = \frac{-7}{6} and a = \frac{-1}{3}

    can you find g(x) ?
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  6. #6
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    We assume that:
    g(x) = ax^2 + bx + c
    and the graph of the function got through 3 points, they are:
    (-2, 2), (0, 1), (1, -2.5)

    g(-2) = 4a - 2b + c = 2;
    g(0) = c = 1
    g(1) = a + b +c = -2.5

    So:
    a = -1; b = -2.5; c = 1;
    g(x) = -x^2 - 2.5x + 1
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  7. #7
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    can anyone figure out f(x) ???
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  8. #8
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     f(x) = 2(x-3)^2
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