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Math Help - congruent? parabola

  1. #1
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    congruent? parabola

    Write an equation that defines each parabola.

    vertex (1,2), opening up, congruent to y = 4x^2 - 5.

    Answer key: y = 4(x-1)^2 + 2

    Please help.

    Thanks.
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  2. #2
    Super Member malaygoel's Avatar
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    Quote Originally Posted by shenton View Post
    Write an equation that defines each parabola.

    vertex (1,2), opening up, congruent to y = 4x^2 - 5.

    Answer key: y = 4(x-1)^2 + 2

    Please help.

    Thanks.
    two parabola are congruent if they are same in evry respect, that is, you can superpose them.
    Now, for two parabola, openint up in the seme direction, the thing that distinguishes them, as far as their shape is concerned is "a"(the distance between the focus and the vertex).
    General equation of a parabola opening up is (x-h)^2 = 4a(y-k) where (h'k) is the vertex of the parabola.
    In your original parabola(y = 4x^2 - 5), a is 1/4
    So a in your parabola is going to be 1/16, since they ought to be congrent.
    So, general equation is (x-1)^2=4*1/16(y-2)


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  3. #3
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    Hello, shenton!

    Write an equation that defines each parabola.
    vertex (1,2), opening up, congruent to y = 4x - 5.

    Answer key: y = 4(x-1) + 2

    If two similarly-oriented graphs are congruent,
    . . one is a "translation" of the other.

    The given parabola has its vertex at (0,-5).
    The new parabola has its vertex at (1,2).

    The parabola has been "moved" 1 unit to the right and 7 units up.

    The new equation is: . y .= .4(x - 1) - 5 + 7

    Therefore: . y .= .4(x -1) + 2

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  4. #4
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    Thanks for the detailed workings!


    (Moderator: I now found this thread - I didn't know it was moved to pre-calculus - for that matter, I didn't know this is a pre-calculus topic. What I do know is this is a quardratic equation problem. Sorry for re-posting the question)
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