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

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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
$y=3(x+7)^2-2$

$= 3(x+7-sqrt(6)/3)(x+7+sqrt(6)/3)$

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