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Math Help - vertex of the parabola y = 3x2 9x + 12, using the formulas for h and k.

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    vertex of the parabola y = 3x2 9x + 12, using the formulas for h and k.

    Find the vertex of the parabola y = 3x2 9x + 12, using the formulas for h and k.

    a.(-3/2,21/4)


    b.(-3/2,-75/4)


    c. (-3/2,129/4)


    d. (3/2,21/4)


    e. none of the above


    thank you!!
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    Help me out please..
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    Quote Originally Posted by skylitejdm View Post
    Find the vertex of the parabola y = 3x2 9x + 12, using the formulas for h and k.

    a.(-3/2,21/4)


    b.(-3/2,-75/4)


    c. (-3/2,129/4)


    d. (3/2,21/4)


    e. none of the above


    thank you!!

    Hi sky,

    What we want to do is put your general equation into vertex form. Let's factor out a 3 from your first two terms like this:

    y=3x^2-9x+12

    y=3(x^2-3x)+12

    Next, we'll complete the square with what we have inside the parentheses:

    y=3\left(x^2-3x+\frac{9}{4}\right)+12-\frac{27}{4}

    Finally, will arrage the above into vertex form.

    y=3\left(x-\frac{3}{2}\right)^2+\frac{21}{4}

    Vertex form is y=a(x-h)^2+k where (h, k) is the vertex of the parabola.

    That would make your vertex \left(\frac{3}{2}, \frac{21}{4}\right)
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