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

Mar 28, 2017

$f \left(x\right) = {\left(x + 2\right)}^{2} - 3$ or ${\left(x - \left(- 2\right)\right)}^{2} - 3$

#### Explanation:

Vertex form of equation is $f \left(x\right) = a {\left(x - h\right)}^{2} + k$

Here, we have $f \left(x\right) = {x}^{2} + 4 x + 1$, hence we have $a = 1$.

So for converting to this form, we complete the square using ${\left(x + a\right)}^{2} = {x}^{2} + 2 a x + {a}^{2}$ for which we have to identify $a$ and then add and subtract ${a}^{2}$. Hence,

$f \left(x\right) = \underline{{x}^{2} + 2 \times 2 \times x + {2}^{2}} - {2}^{2} + 1$

$= {\left(x + 2\right)}^{2} - 4 + 1$

$= {\left(x - \left(- 2\right)\right)}^{2} - 3$