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What is the vertex form of $y = x^{2} + 4 x + 2$ $y=x^2 + 4x + 2$ ?

1 Answer

Nov 16, 2015

$y = {(x - (- 2))}^{2} + (- 2)$ $y=(x-(-2))^2+(-2)$

Explanation:

The general vertex form is
$XXX y = a (x - p) + q$ $color(white)("XXX")y=a(x-p)+q$
with vertex at $(p, q)$ $(p,q)$

$y = x^{2} + 4 x + 2$ $y=x^2+4x+2$

Complete the square:
$XXX = x^{2} + 4 x + 4 - 2$ $color(white)("XXX")=x^2+4x+4-2$

$XXX = {(x + 2)}^{2} - 2$ $color(white)("XXX")=(x+2)^2-2$

Adjust signs to get vertex form:
$XXX = {(x - (- 2))}^{2} + (- 2)$ $color(white)("XXX")=(x-(-2))^2+(-2)$
with vertex at $(- 2, - 2)$ $(-2,-2)$

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