Question 175023
The vertex form is 
{{{y = a(x-h)^2 + k}}} where the vertex is at (h,k)
{{{y = ax^2 - 2ahx + ah^2 + k}}}
{{{y = x^2 - 2hx + h^2 + k/a}}}
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Given that one of the roots is
{{{(1 + sqrt(3))/3i}}}
The other is
{{{(1 - sqrt(3))/3i}}}
If {{{x[1]}}} and {{{x[2]}}} are the roots
{{{(x - x[1])(x - x[2]) = x^2 - (x[1] + x[2])x + (x[1]*x[2])}}}
{{{x^2 - 2/(3i)x + 2/9}}}
{{{h^2 + k/a = 2/9}}}
{{{-2h = -2/(3i)}}}
{{{h = 1/(3i)}}}
{{{h = -i/3}}}
{{{a = 1}}}
{{{h^2 + k/a = 2/9}}}
{{{(-i/3)^2 + k = 2/9}}}
{{{1/9 + k = 2/9}}}
{{{k = 1/9}}}
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The vertex form is 
{{{y = a(x-h)^2 + k}}} where the vertex is at (h,k)
{{{y = (x + (i/3))^2 + 1/9}}} answer
{{{ graph( 500, 500, -10, 10, -10, 10, x^2 + (2i/3)*x + 4/9) }}}
I think my method is OK, I
may have messed up the algebra