How do you convert vertex form to factored form #y = 3(x+7)^2 - 2#?

Question

77668 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-01T19:03:13

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)#