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

Mar 31, 2017

$\text{Vertex :} \left(1 , - 6\right)$

#### Explanation:

$\text{given function } y = - {x}^{2} + 2 x - 7$

$\text{derivate the function y with respect to x and make equal to zero.}$

$\frac{d y}{d x} = 0$

$\frac{d}{d x} \left(- {x}^{2} + 2 x - 7\right) = 0$

$- 2 x + 2 = 0$

$- 2 x = - 2$

$x = \frac{2}{2}$

$x = 1$

$\text{plug x=1 in the function } y = - {x}^{2} + 2 x - 7$

$y = - {1}^{2} + 2 \cdot 1 - 7$

$y = - 1 + 2 - 7$

$y = - 6$