Question 130120
To find the x-coordinate of the vertex, simply average the two roots.



{{{2 - 1.415i+ 2 + 1.415i}}} Add the two roots



{{{(2+2) +(1.415i- 1.415i)}}} Group like terms



{{{4 - 0i}}} Combine like terms



{{{4}}} Simplify



So it turns out that when you add any two complex conjugates together you will get a real answer.



Now divide the answer by 2


{{{4/2=2}}}


So the x-coordinate of vertex is 2







note:

Remember the quadratic formula is 


{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}} and the formula for the x-coordinate of the vertex is {{{x=-b/(2a)}}}. Notice if you add the two roots the square root part cancels out to to give you {{{-b/(2a)}}}. So this shows how the quadratic formula and the vertex are related.