Question

what is the domain of this quadratic function?
options:
{x|x ≤ 3}
{x|x ≤ 4}
{x|-3 ≤ x ≤ 1}
all real numbers

Explanation:

Step1: Recall domain definition

The domain of a function is the set of all possible x - values for which the function is defined. For a quadratic function (a parabola), if it is a polynomial function, the domain of any polynomial function (including quadratic functions) is all real numbers. This is because there are no restrictions on the values of x that we can plug into a quadratic function \(y = ax^{2}+bx + c\) (where \(a
eq0\)) - we can substitute any real number for x and get a real - valued output.

Step2: Analyze the graph

Looking at the graph of the quadratic function (parabola) given, we can see that the parabola extends infinitely to the left and to the right along the x - axis (the arrows on the ends of the parabola indicate that it continues indefinitely in the horizontal direction). There are no breaks or restrictions on the x - values that the parabola covers. So, the set of all x - values for this quadratic function is all real numbers.

Answer:

all real numbers