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

1 Answer
Mar 21, 2017

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]