# What is the vertex form of y=2x^2 + 2x + 12?

Feb 23, 2016

$y = 2 {\left(x + \frac{1}{2}\right)}^{2} + \frac{23}{2}$

#### Explanation:

The standard form of a quadratic function is $y = a {x}^{2} + b x + c$

The function $y = 2 {x}^{2} + 2 x + 12 \text{ is in this form }$

and by comparison , a = 2 , b = 2 and c = 12

The vertex form of the equation is $y = a {\left(x - h\right)}^{2} + k$
where (h , k ) are the coordinates of the vertex.

x-coord of vertex (h ) $= \frac{- b}{2 a} = \frac{- 2}{4} = - \frac{1}{2}$

and y-coord (k) =$2 {\left(- \frac{1}{2}\right)}^{2} + 2 \left(- \frac{1}{2}\right) + 12 = \frac{1}{2} - 1 + 12 = \frac{23}{2}$

here $\left(h , k\right) = \left(- \frac{1}{2} , \frac{23}{2}\right) \mathmr{and} a = 2$

$\Rightarrow y = 2 {\left(x + \frac{1}{2}\right)}^{2} + \frac{23}{2} \text{ is equation in vertex form }$