# How do you find the axis of symmetry, graph and find the maximum or minimum value of the function y=x^2 - 2x - 1 ?

Feb 9, 2017

Symmetry: $x = 1$ ; Maximum value is $\infty$ , Minimum value is $- 2$

#### Explanation:

This is a parabola opening upwards $a > 0$

y= x^2-2x-1 (ax^2+bx+c); a=1 ; b = -2 ; c= -1
Discriminant $D = {b}^{2} - 4 a c = 4 + 4 = 8$
Vertex (x,y) ; x= (-b)/(2a)= 2/2=1 ; Putting $x = 1$ we can get $y = {1}^{2} - 2 \cdot 1 - 1 = - 2 \therefore$ Vertex is at $\left(1 , - 2\right) \therefore x = 1$ is the axis of symmetry.

$a > 0 \therefore$ Maximum value is $\infty$ ; Minimum value is $y = - \frac{D}{4 a} = - \frac{8}{4} = - 2$ at $x = - \frac{b}{2 a} = \frac{- \left(- 2\right)}{2} = 1$ i.e Vertex is the minimum point.
Symmetry: $x = 1$ ; Maximum value is $\infty$ , Minimum value is $- 2$ graph{x^2-2x-1 [-10, 10, -5, 5]} [Ans]