This is the vertex form of the standardised#" " y=ax^2+bx+c#
Multiplying out the brackets the we have #" "y=3x^2+18x+24#
As the #3x^2# is positive the graph is of general shape #uu#
#color(blue)("Determine the vertex using the questions equation format")#
Given:#" "y=3(xcolor(red)(+3))^2color(green)(-3)#
#x_("vertex")=(-1)xxcolor(red)((+3)) = -3#
#y_("vertex")=color(green)(-3)#
Vertex#->(x,y)=(-3,-3)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the x-intercepts")#
set #y=0#
#=>0=3(x+3)^2-3#
#3=3(x+3)^2#
#(x+3)^2=1#
#x+3=+-sqrt((1)#
#x=-3+-1#
#x=-4 and -2#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine y-intercept")#
Set #x=0#
#y= 3(0+3)^2-3#
#y=27-3=24#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Foot note")#
Using the format #y=3x^2+18x+24#
#x_("vertex")=(-1/2)xx(18/3)=-3#
