Question

the graph of a quadratic function with vertex (1, 0) is shown in the figure below. find the domain and the range. write your answers as inequalities, using x or y as appropriate. or, you may instead click on \empty set\ or \all reals\ as the answer. (a) domain: (b) range:

Explanation:

Step1: Determine the domain

The graph of a quadratic function (a parabola) extends infinitely in the horizontal direction (left and right) unless there are restrictions, but in this case, since it's a standard quadratic function graph (no horizontal restrictions shown), the domain includes all real numbers. So, the domain is all real numbers, which can be written as \( -\infty < x < \infty \) or simply "All reals" for \( x \).

Step2: Determine the range

The vertex of the parabola is at \( (1, 0) \), and the parabola opens downward (since the graph has a maximum at the vertex and goes downwards from there). For a downward - opening parabola, the \( y \) - values (the range) are less than or equal to the \( y \) - coordinate of the vertex. The \( y \) - coordinate of the vertex is 0, so the range is \( y\leq0 \).

Answer:

(a) domain: All reals (or \( -\infty < x < \infty \))
(b) range: \( y\leq0 \)