# What is the vertex of the parabola y= x^2 - 5x - 4?

Mar 29, 2018

$y = {\left(x - \frac{5}{2}\right)}^{2} - \frac{41}{4}$

#### Explanation:

$y = {x}^{2} - 5 x - 4$
x-coordinate of vertex:
$x = - \frac{b}{2 a} = \frac{5}{2}$
y-coordinate of vertex:
$y \left(\frac{5}{2}\right) = \frac{25}{4} - \frac{25}{2} - 4 = - \frac{25}{4} - \frac{16}{4} = - \frac{41}{4}$
Vertex form:
$y = {\left(x - \frac{5}{2}\right)}^{2} - \frac{41}{4}$