Question

find the range of this quadratic function.

\\y = x^2 + 2\\

\\-2 \le y < \infty\\

\\2 \le y < \infty\\

Explanation:

Identify the vertex of the parabola

$$ \text{Vertex } (h, k) = (0, 2) $$

Determine the direction of opening

$$ a = 1 > 0 \implies \text{Opens upward} $$

Find the minimum value and range

$$ y \ge 2 \implies 2 \le y < \infty $$

Answer:

• \(-2 \le y < \infty\)
• \(2 \le y < \infty\) (Correct answer)