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

1 Answer
Feb 9, 2017

Symmetry: x=1 ; Maximum value is oo , 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^2-4ac=4+4=8
Vertex (x,y) ; x= (-b)/(2a)= 2/2=1 ; Putting x=1 we can get y= 1^2-2*1-1= -2 :. Vertex is at (1 , -2) :. x=1 is the axis of symmetry.

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