# What is the vertex form of y=x^2-x-72 ?

Jul 24, 2016

$y = {\left(x - \frac{1}{2}\right)}^{2} - 72 \frac{1}{4}$

#### Explanation:

Given

$y = {x}^{2} - x - 72$

Find the Vertex

X-cordinate of the vertex

$x = \frac{- b}{2 a} = \frac{- \left(- 1\right)}{2 \times 1} = \frac{1}{2}$
At x=1/2; y=(1/2)^2-1/2-72=1/4-1/2-72=-72 1/4

Vertex for of the quardratic equation is

$y = a \left(x - h\right) + k$

Where $h$ is $x$cordinate and $k$ is $y$ coordinate
$a$ is the coefficient of ${x}^{2}$

$h = \frac{1}{2}$
$k = - 72 \frac{1}{4}$
$a = 1$

Substitute these values in the formula

$y = {\left(x - \frac{1}{2}\right)}^{2} - 72 \frac{1}{4}$