Question

what is the range of this quadratic function?
{y|y ≥ -8} {y|y ≤ -8}
{y| -8 ≤ y ≤ 10} all real numbers

Explanation:

Step1: Analyze the parabola's direction

The parabola opens upwards (since the arms of the parabola point upwards), so the vertex is the minimum point.

Step2: Identify the vertex's y - coordinate

From the graph, the vertex of the parabola has a y - coordinate of - 8.

Step3: Determine the range

For a parabola that opens upwards, the range is all real numbers greater than or equal to the y - coordinate of the vertex. So the range of the quadratic function is all y such that \(y\geq - 8\), or in set notation \(\{y|y\geq - 8\}\).

Answer:

\(\{y|y\geq - 8\}\)