Given
#color(white)("XXX")y=color(brown)((2x+1)(x+6))+6x#
(first converting into standard form):
#color(white)("XXX")rArr y=color(brown)(2x(x+6)+1(x+6))+6x#
#color(white)("XXX")rArr y =color(brown)( 2x^2+12x+x+6)+6x#
#color(white)("XXX")rArr y= 2x^2+19x+6#
Remember the vertex form is #y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)# with vertex at #(color(red)(a),color(blue)(b))#
Extract the #color(green)(m)# factor
#color(white)("XXX")y=color(green)(2)(x^2+19/2x)+6#
Complete the square
#color(white)("XXX")y=color(green)(2)(x^2+19/2x+(19/4)^2)+6-2*(19/4)^2#
Simplify into vertex form
#color(white)("XXX")y=color(green)(2)(x-(color(red)(-19/4)))^2+(color(blue)(-313/8))#
Since #-19/4# is about #-5#
and #-313/8# is about #-39#
the graph below of the original equation supports this answer.
graph{(2x+1)(x+6)+6x [-19.8, 12.24, -40.05, -24.01]}
