Write as:#" "y=2x^2-12x +0#
#color(blue)("The y intercept is at y=0")#
y =0 at x=0
#color(brown)("so one of the x intercepts is at x=0")#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
write as #y=2(x^2-6x)#
#color(blue)(x_("vertex") = (-1/2)xx(-6) = +3)#
#color(brown)(y=2x^2-12xcolor(green)(" "->" "y_("vertex")=2(3)^2-12(3) =-18))#
#color(blue)(y_("vertex")=-18)#
#color(blue)("Vertex"->(x,y)=(3,-18))#
#color(brown)("As the coefficient of "x^2" is positive then the general shape of")##color(brown)("the graph is " uu)# #color(blue)(" Thus the vertex is a Minimum")#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#x_("intercpt")->y=0#
# => 0=2(x^2-6x)#
Divide both sides by 2
#=>0/2=2/2(x^2-6x)#
But #0/2=0" and "2/2=1#
#=>0=(x^2-6x)#
Factor out #x#
#=>0=x(x-4)#
For #y=0 ; x=0" and/or "x=+4#
#color(blue)(x_("intercepts")-> x=0; x=4)#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
