Question

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

Answer 1

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]