#"given a quadratic in standard form ";ax^2+bx+c;a!=0#
#"then the x-coordinate of the vertex which is also the"#
#"axis of symmetry can be found using"#
#•color(white)(x)x_(color(red)"vertex")=-b/(2a)#
#"here "a=-3,b=-12,c=-3#
#rArrx_("vertex")=-(-12)/-6=-2#
#rArr"axis of symmetry is "x=-2#
#"the vertex lies on the axis of symmetry thus substituting"#
#"x = - 2 into the equation gives y-coordinate"#
#rArry_("vertex")=-3(-2)^2-12(-2)-3=9#
#rArrcolor(magenta)"vertex "=(-2,9)#
#"to determine if vertex is maximum/minimum"#
#• " if "a>0" then minimum turning point"#
#• " if "a<0" then maximum turning point"#
#"here "a=-3<0#
#rArr-3x^2-12x-3" has a maximum at "(-2,color(red)(9))#
#"with maximum value "=9#
graph{-3x^2-12x-3 [-20, 20, -10, 10]}
