Final answer:
The question involves the properties of a quadratic function in Algebra, specifically addressing the vertex, roots, domain, and range, which are fundamental in understanding the function's graph on a coordinate plane.
Step-by-step explanation:
The subject matter presented in the question is related to the properties of a quadratic function, which is a topic in Algebra, a branch of Mathematics. Specifically, the properties in the question pertain to the vertex, roots, domain, and range of a quadratic function, which are essential in understanding its graph and representation on the coordinate plane.
The vertex form of a quadratic function can be written as f(x) = a(x - h)2 + k, where (h, k) is the vertex, and the roots (also called zeroes) are the values where the function equals zero. The domain of a quadratic function is always all real numbers, indicating that you can plug any real number into the function. The range is the set of all possible output values, which, depending on the direction in which the parabola opens, is limited to values either greater than or less than the vertex's y-coordinate.
A parabola that opens upwards has a range of [y-value of vertex, ∞), as illustrated by the range provided in the question (y > -22). In the given context, the inequality domain and interval domain confirm that the function is defined for all real numbers, while the inequality and interval range indicate that the output values of the function are greater than or equal to -22.