Question

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

Answer 1

$\large\begin{array}{l} \textsf{In the following equation}\\\\ \mathsf{y=x^2-6x+1}\\\\ \textsf{x can be any real number (there's no restriction for the domain).}\\\\\\ \textsf{Answer: All real numbers.} \end{array}$


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Answer 2

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