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]