# What are the coordinates of the vertex of y = x^2 - 4x - 5?

Apr 28, 2015

$y = {x}^{2} - 4 x - 5$
is a parabola with a slope (for arbitrary values of $x$) given by the expression
$\frac{\mathrm{dy}}{\mathrm{dx}} = 2 x - 4$

This slope is equal to $0$ at the vertex of the parabola
$2 x - 4 = 0$
$\rightarrow x = 2$

When $x = 2$ the equation for the parabola gives us
$y = {\left(2\right)}^{2} - 4 \cdot \left(2\right) - 5$

$= - 9$

So the coordinates of the vertex of the parabola are
$\left(2 , - 9\right)$