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

Mar 22, 2017

"Vertex{-3.5" , "-4.25}

#### Explanation:

$y = {\left(x + 2\right)}^{2} + 3 x + 4$

$y = {x}^{2} + 4 x + 4 + 3 x + 4$

$y = {x}^{2} + 7 x + 8 \text{ (1)}$

$\frac{d y}{d x} = 0$

$\frac{d y}{d x} = 2 x + 7 = 0$

$2 x + 7 = 0$

$2 x = - 7$

$x = - \frac{7}{2} = - 3.5$

$\text{use (1)}$

$y = {\left(- \frac{7}{2}\right)}^{2} - 7 \left(\frac{7}{2}\right) + 8$

$y = \frac{49}{4} - \frac{49}{2} + 8$

$y = \frac{49 - 98 + 32}{4}$

$y = - \frac{17}{4} = - 4.25$

"Vertex{-3.5" , "-4.25}