# What is the vertex of f(x)=x^2+4x+3?

Sep 26, 2014

The vertex of $f$ is $\left(- 2 , - 1\right)$.

Let us look at some details.

The vertex of $f \left(x\right) = a {x}^{2} + b x + c$ can be found by

$\left(- \frac{b}{2 a} , f \left(- \frac{b}{2 a}\right)\right)$.

For $f \left(x\right) = {x}^{2} + 4 x + 3$,

$- \frac{b}{2 a} = - \frac{4}{2 \left(1\right)} = - 2$

So, the vertex is

$\left(- 2 , f \left(- 2\right)\right) = \left(- 2 , - 1\right)$