Question

what is the range of this quadratic function? {y|y ≤ 2} {y|y ≤ 6} {y|y ≥ 6} all real numbers

Explanation:

Step1: Analyze the parabola's direction and vertex

The quadratic function's graph is a parabola opening downward (since the ends point down), so the vertex is the maximum point. The vertex's y - coordinate is 6.

Step2: Determine the range

The range of a function is the set of all possible y - values. For a downward - opening parabola, the y - values start from negative infinity (or as low as the graph goes) up to the maximum y - value at the vertex. So the y - values are all real numbers less than or equal to 6.

Answer:

$\{y|y \leq 6\}$ (corresponding to the option: {y|y ≤ 6})