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How do you convert vertex form to factored form ##y = 3(x+7)^2 - 2##?
Expand the vertex form into standard quadratic form; then use the quadratic root formula to determine the roots.
##y=3(x+7)^2-2##
##=3(x^2+14x+49)-2##
##= 3x^2+42x+145##
Using the formula for determining roots (and a very sharp pencil) ##(-b+-sqrt(b^2-4ac))/(2a)##
gives roots at ##x= -7+sqrt(6)/3## and ##x= -7-sqrt(6)/3##
So ##x+7-sqrt(6)/3## and ##x+7+sqrt(6)/3## are factors of the original equation
Fully factored form ##y=3(x+7)^2-2##
##= 3(x+7-sqrt(6)/3)(x+7+sqrt(6)/3)##