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

Apr 14, 2017

Vertex form is $y = {\left(x + \frac{7}{2}\right)}^{2} - \frac{57}{4}$ and vertex is $\left(- 3 \frac{1}{2} , - 14 \frac{1}{4}\right)$

#### Explanation:

$y = {x}^{2} + 7 x - 2$

= x^2+2×7/2×x+(7/2)^2-(7/2)^2-2

= ${\left(x + \frac{7}{2}\right)}^{2} - \frac{49}{4} - 2$

= ${\left(x + \frac{7}{2}\right)}^{2} - \frac{57}{4}$

Hence, vertex form is $y = {\left(x + \frac{7}{2}\right)}^{2} - \frac{57}{4}$ and vertex is $\left(- \frac{7}{2} , - \frac{57}{4}\right)$ or $\left(- 3 \frac{1}{2} , - 14 \frac{1}{4}\right)$