# What is the vertex form of y= x^2+7x-30 ?

Mar 31, 2017

$\left(y + \frac{89}{4}\right) = {\left(x + \frac{7}{2}\right)}^{2}$

#### Explanation:

$y = {x}^{2} + 7 x - 10$
transpose -10 to the right side of the equation, from negative it will change its sign into positive

$y + 10 = {x}^{2} + 7 x$

Complete the square of the right side of the equation
Get half of the coefficient of x, then raise it to the second power.

Mathematically as follows: ${\left(\frac{7}{2}\right)}^{2}$= $\frac{49}{4}$

$\frac{49}{4}$ to both sides of the equation
$y + 10 + \frac{49}{4} = {x}^{2} + 7 x + \frac{49}{4}$
$\left(y + \frac{89}{4}\right) = {\left(x + \frac{7}{2}\right)}^{2}$ $a n s w e r$