Question 875255
The leading term in general form or the value of the coefficient on the squared binomial will tell you if the graph or equation has vertex as a minimum or as a maximum.  y=ax^2+bx+c  opens upward for a>0 and opens downward for a<0.


You should study more about how to complete the square to put a quadratic equation into standard form.  The term to complete the square for your equation is 4; but you first need to factor the 2 from the two terms containing x.
You should find {{{y=-2(x-2)^2+13}}}.


Read and study this:  <a href="http://www.algebra.com/tutors/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev">Completing the Square to Solve General Quadratic Equation - includes showing how to convert to standard form.</a>