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A **quadratic polynomial** is a polynomial of degree 2. It has the general form \(ax^2 + bx + c\), where **a**, **b**, and **c** are constants, and **a 鈮� 0**. Quadratic polynomials are called 'quadratic' because they involve terms with the variable raised to the power of 2. In our exercise, we deal with the quadratic polynomial **x虏 - 6x + 7**.

The graph of a quadratic polynomial is a parabola. If the leading coefficient **a** is positive, the parabola opens upwards. If **a** is negative, it opens downwards. Understanding the shape and properties of quadratic graphs helps in analyzing their behaviors and domains. The domain of any polynomial, including a quadratic polynomial, consists of all real numbers. This means it can take any value from negative infinity to positive infinity.

The **absolute value** of a number is its distance from zero on the number line, regardless of direction. In mathematical terms, the absolute value of a number **x** is denoted as \(|x|\). For example:

- \(|3| = 3\) (since 3 is three units away from zero)
- \(|-3| = 3\) (since -3 is also three units away from zero)

When dealing with functions, the absolute value function takes any real number and converts it to its non-negative counterpart. This is particularly useful in our exercise where we have **g(x) = |x虏 - 6x + 7|**. Even though **x虏 - 6x + 7** can be negative or positive depending on the value of x, the absolute value ensures the output of **g(x)** is always non-negative.

**Real numbers** include all the numbers on the continuous number line, from negative infinity to positive infinity. The set of real numbers, denoted by **鈩�**, encompasses rational numbers (such as fractions and integers) and irrational numbers (like the square root of 2 or 蟺).

When determining the domain of a function like **g(x) = |x虏 - 6x + 7|**, it's crucial to note that the quadratic expression **x虏 - 6x + 7** and the absolute value function are both always defined for all real numbers. Thus, the function **g(x)** is valid for any real number **x**.

In simpler words, you can plug any real number into **g(x) = |x虏 - 6x + 7|** and get a valid output. Hence, the domain of the function is all real numbers, written in interval notation as \((-\text{鈭瀩, \text{鈭瀩)\).