Question

what is the range of this quadratic function? the graph is a parabola opening downward with vertex at (2,6). the options are {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). The vertex (highest point) has a y - coordinate of 6.

Step2: Determine the range

For a downward - opening parabola, the range consists of all y - values less than or equal to the y - coordinate of the vertex. So the range is all real numbers y such that \(y\leq6\), or in set - builder notation \(\{y|y\leq6\}\).

Answer:

\(\{y|y\leq6\}\)