To determine the domain of the equation y = x² + 6x + 1, we first need to understand what the domain of a function represents. The domain of a function is the set of all possible input values (x-values) that will produce valid output values (y-values).
In this case, the equation is a quadratic function, which is a polynomial of degree 2. One of the key characteristics of polynomial functions is that they are defined for all real numbers. This means that we can plug any real number into the equation without running into any restrictions, such as division by zero or square roots of negative numbers.
Thus, the domain of the function y = x² + 6x + 1 is all real numbers.
In interval notation, we can express this as:
(−∞, ∞)