# What is the vertex form of y= 7x^2+2x+12 ?

May 16, 2017

$y = 7 {\left(x + \frac{1}{7}\right)}^{2} + \frac{83}{7}$

#### Explanation:

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

We have $y = 7 {x}^{2} + 2 x + 12$

= $7 \left({x}^{2} + 2 \times \frac{1}{7} \times x + {\left(\frac{1}{7}\right)}^{2} - {\left(\frac{1}{7}\right)}^{2}\right) + 12$

= $7 {\left(x + \frac{1}{7}\right)}^{2} - 7 {\left(\frac{1}{7}\right)}^{2} + 12$

= $7 {\left(x + \frac{1}{7}\right)}^{2} - \frac{1}{7} + 12$

= $7 {\left(x + \frac{1}{7}\right)}^{2} + \frac{83}{7}$

i.e. $y = 7 {\left(x + \frac{1}{7}\right)}^{2} + \frac{83}{7}$