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Math Help - Algebra-quadratics

  1. #1
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    Algebra-quadratics

    I really unsure how to start with this, any help would be much appreciated


    Find the vertex form of the quadratic function y = 3x^2 + 5x + 9



    Find the vertex of the parabola which is the graph of the quadratic function y = -2x^2 + 4x + 6
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  2. #2
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    Vertex form is when you complete the square.

    y = 3x^2 + 5x + 9

    \Rightarrow y = 3(x^2 + \frac{5}{3}x + 3)

    \Rightarrow y = 3[(x+\frac{5}{6})^2 - (\frac{5}{6})^2 + 3]

    \Rightarrow y = 3[(x+\frac{5}{6})^2 - \frac{25}{36} + 3]

    \Rightarrow y = 3[(x+\frac{5}{6})^2 + \frac{83}{36}]\quad (because 3 = 108/36)

    \Rightarrow y = 3(x+\frac{5}{6})^2 + \frac{83}{12}

    For the above example, the vertex is at x = -\frac{5}{6}. It is the number which makes the squared bracket = 0. For Q2 do the same as above then you can find the vertex.
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