# What is the vertex form of y=x^2+8x+14 ?

Jan 30, 2016

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

#### Explanation:

the standard form of a parabola is $y = a {x}^{2} + b x + c$

compare to $y = {x}^{2} + 8 x + 14$

to obtain a = 1 , b= 8 and c = 14

The vertex form is : $y = a {\left(x - h\right)}^{2} + k$

where (h , k ) are the coordinates of the vertex.

x-coord of vertex $= - \frac{b}{2 a} = - \frac{8}{4} = - 2$

the y-coord = ${\left(- 2\right)}^{2} + 8 \left(- 2\right) + 14 = 8 - 16 + 14 = - 2$

equation is : $y = a {\left(x + 4\right)}^{2} - 2$

in this question(see above ) a = 1

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