Question 709270
EDIT: Fixed the sign mistake.


First, factor.  Then complete the square.

{{{y=-3(x^2+3x+4)}}}
The square to add and subtract is {{{(3/2)^2}}}.

{{{y=-3(x^2+3x+(3/2)^2 +4-(3/2)^2)}}}
{{{y=-3((x+(3/2))^2+(7/4))}}}
{{{y=-3(x+3/2)^2+7/4}}}
{{{y=-3(x+3/2)^2-21/4}}}
{{{y=-3(x+3/2)^2-5&1/4)}}}



The value of "h" is {{{-(3/2)}}} and the value of "k" is {{{-(21/4)}}} or {{{-(5&1/4)}}}.
The vertex is ({{{-(3/2)}}},{{{-5&1/4}}})