Question

What is the vertex form of `y=x^2 + 4x + 2`?

Answer 1

`y=(x-(-2))^2+(-2)`

Explanation:

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

`y=x^2+4x+2`

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

`color(white)("XXX")=(x+2)^2-2`

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