How do you find the domain and range of #y=(x^2) - 6x + 1#?

1 Answer
Mar 21, 2017

Answer:

Domain: All real numbers i.e #(-oo,oo)#
Range: Real numbers #>= -8 or [-8, +oo)#

Explanation:

#y=x^2-6x+1 ; a=1 ,b= -6 ; c=1 [ax^2+bx+c]#
Domain (possible values of x) : All real numbers i.e #(-oo,oo)#
Range: This is a parabola of which vertex(x) is #-b/2a = 6/2=3# and Vertex(y) is #y= 3^2- 6*3 +1= -8#

So vertex is at #(3,8)# Since #a=+ive#. the parabola opens upward and #y= - 8# is the minimum value and #+oo# is maximum value
So range is #y >= -8 or [-8, +oo)# graph{x^2-6x+1 [-20, 20, -10, 10]} [Ans]