Question

what is the range of this quadratic function?
options:
{y|y ≥ 1}
{y|y ≥ 5}
{y|1 ≤ y ≤ 10}
all real numbers

Explanation:

Step1: Analyze the parabola's direction and vertex

The quadratic function's graph is a parabola opening upwards (since the arms go up), so it has a minimum point (vertex). The vertex's y - coordinate is the minimum value of the function. From the graph, the vertex is at \( y = 1 \) (visually, the lowest point on the parabola has a y - value of 1).

Step2: Determine the range

For a parabola opening upwards, the range is all real numbers greater than or equal to the y - coordinate of the vertex. So the range of the function is all y such that \( y\geq1 \), which is \( \{y|y\geq1\} \).

Answer:

\(\{y|y\geq1\}\)