Question

what is the solution set of the quadratic inequality \\(f(x) \ge 0\\)?

\\(\\{x \mid x \in \mathbb{r}\\}\\)

\\(\varnothing\\)

\\(\\{x \mid x = -3\\}\\)

\\(\\{x \mid x = 3\\}\\)

Explanation:

Identify the vertex and orientation of the parabola

$$ \text{Vertex} = (-3, 0) $$

$$ \text{Parabola opens upwards} $$

Determine the range of the function

$$ f(x) \ge 0 \quad \forall x \in \mathbb{R} $$

Find the solution set for the inequality

$$ \{x \mid x \in \mathbb{R}\} $$

Answer:

• (A) \(\{x \mid x \in \mathbb{R}\}\) (Correct answer)
• (B) \(\varnothing\)
• (C) \(\{x \mid x = -3\}\)
• (D) \(\{x \mid x = 3\}\)