Question

a graph of quadratic function y = f(x) is shown below. what is the solution set of the quadratic inequality f(x) ≥ 0? {x| x ∈ ℝ} ∅

Explanation:

Step1: Analyze the graph's position

The quadratic function \( y = f(x) \) is a parabola opening upwards (since the arms go up) and its vertex is on the x - axis at \( x=-3 \). For all real values of \( x \), the graph of the function is either on or above the x - axis (because the parabola opens upwards and touches the x - axis at its vertex, and for other points, \( y\geq0 \)).

Step2: Determine the solution set

The inequality \( f(x)\geq0 \) asks for all \( x \) values where the function's output is greater than or equal to zero. From the graph, since the parabola is always on or above the x - axis ( \( y\geq0 \) for all \( x\in\mathbb{R} \) ), the solution set is all real numbers.

Answer:

\(\{x|x\in\mathbb{R}\}\)