Question

what is the domain of this quadratic function?

Explanation:

Step1: Recall domain definition

The domain of a function is the set of all possible \( x \)-values for which the function is defined.

Step2: Analyze quadratic graph

For a quadratic function (parabola), the graph extends horizontally (along the \( x \)-axis) to the left and right without any breaks or restrictions (unless there's a specific context, but here it's a standard parabola). So the \( x \)-values can be any real number.

Step3: Express domain

In interval notation, all real numbers are represented as \( (-\infty, \infty) \), or in set notation as \( \{x | x \in \mathbb{R}\} \).

Answer:

The domain of the quadratic function is all real numbers, which can be written as \( (-\infty, \infty) \) (or \( \{x | x \text{ is a real number}\} \)).