Question

How do you write `f(x)=x^2+4x+1` in vertex form?

Answer 1

`f(x)=(x+2)^2-3` or `(x-(-2))^2-3`

Explanation:

Vertex form of equation is `f(x)=a(x-h)^2+k`

Here, we have `f(x)=x^2+4x+1`, hence we have `a=1`.

So for converting to this form, we complete the square using `(x+a)^2=x^2+2ax+a^2` for which we have to identify `a` and then add and subtract `a^2`. Hence,

`f(x)=ul(x^2+2xx2xx x+2^2)-2^2+1`

`=(x+2)^2-4+1`

`=(x-(-2))^2-3`