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Math Help - quadratics function

  1. #1
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    quadratics function

    Given the quadratic y = 3x2 + 12x - 7, find the inverse of the quadratic. Graph both the original function and the inverse on the same set of axes. State the domain and range of both
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  2. #2
    Senior Member euclid2's Avatar
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    Quote Originally Posted by william View Post
    Given the quadratic y = 3x2 + 12x - 7, find the inverse of the quadratic. Graph both the original function and the inverse on the same set of axes. State the domain and range of both
     y=3x^2 +12x - 7
    To find the inverse ,  f^-1(x) make a table of values and switch the values of x for the values of y.
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by william View Post
    Given the quadratic y = 3x2 + 12x - 7, find the inverse of the quadratic. Graph both the original function and the inverse on the same set of axes. State the domain and range of both
    To find the inverse, the technique of completing the square is necessary!

    I'll start you off:

    y=3x^2+12x-7\implies x=3y^2+12y-7\implies x+7=3(y^2+4y)\implies \tfrac{1}{3}(x+7)=y^2+4y

    Try to take it from here.

    Now, here's the graph of the functions:



    (The functions are inverses, since are reflections about the line y=x [in green])

    --Chris
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  4. #4
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    Quote Originally Posted by Chris L T521 View Post
    To find the inverse, the technique of completing the square is necessary!

    I'll start you off:

    y=3x^2+12x-7\implies x=3y^2+12y-7\implies x+7=3(y^2+4y)\implies \tfrac{1}{3}(x+7)=y^2+4y

    Try to take it from here.

    Now, here's the graph of the functions:



    (The functions are inverses, since are reflections about the line y=x [in green])

    --Chris
    How exactly do I complete the square and what method did you use?
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