Given;#" "y=3x^2+12x+4#
#color(blue)(y_("intercept")" at "x=0 -> y=4)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine "y_("intercept") " & Vertex"#
Transpose equation into vertex form
Standard form #y=ax^2+bx+c#
Vertex form #y=a(x+b/(2a))^2+c - [(b/2)^2]#
#y=3(x+2)^2+4 -12#
#y=3(x+2)^2-8#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)(x_("vertex")->(-1)xxb/(2a)" "->" "(-1)xx(2) = -2)#
#color(blue)(y_("vertex")-> c - [(b/2)^2]" "->" "-8#
#color(blue)("Vertex "->(x,y)->(-2,-8)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine " x_("intercepts"))#
Set #" "color(brown)(y=3(x+2)^2-8)" to "color(green)( 3(x+2)^2-8 =0)#
#(x+2)^2=8/3#
Take square roots of both sides
#x+2=+-sqrt(8/3)#
#x= +-sqrt(8/3)-2" " -> sqrt(8)/sqrt(3)xxsqrt(3)/sqrt(3) = sqrt(24)/3#
#x=+-sqrt(24)/3-2" "# Exact values
#x~~3.633" and "-0.367#
