Question

Identify the domain of the equation y = x2 − 6x + 1.

x ≤ 3
x ≥ −8
x ≥ −2
All real numbers

Answer 1

we have

`y=x^(2)-6x+1`

this is the equation of a vertical parabola open upward

Convert into vertex form

`y-1=x^(2)-6x`

`y-1+9=x^(2)-6x+9`

`y+8=(x-3)^(2)`

`y=(x-3)^(2)-8`

The vertex is the point
`(3,-8)` ----> is a minimum

The range of the function is the interval--------> [-8,∞)

that means------> all real numbers greater than or equal to
`-8`

The domain of the function is the interval-----> (-∞,∞)

that means------> all real numbers

therefore

the answer is the option

All real numbers

see the attached figure to better understand the problem