Question

1. the set of all real numbers represented by $(-\infty, \infty)$ is typically the ______ of a quadratic function.
2. the ______ of a quadratic function describes whether the parabola opens upwards or downwards.
3. in interval notation, when a value is not included in the domain or range of a function, we use ______.

Explanation:

1. For a quadratic function $f(x)=ax^2+bx+c$, there are no restrictions on the real numbers $x$ can take, so its domain is all real numbers $(-\infty, \infty)$.
2. The coefficient $a$ of the $x^2$ term in $f(x)=ax^2+bx+c$ determines the direction the parabola opens: positive $a$ opens upward, negative $a$ opens downward.
3. In interval notation, parentheses (round brackets) are used to indicate that an endpoint is not included in the set.

Answer:

1. domain
2. leading coefficient (or coefficient of $x^2$ term)
3. parentheses (or round brackets)