Question

question
determine the domain on which the following function is increasing.
(image of a parabola graph)
answer
(input box and submit answer button with various math symbols below)

Explanation:

Step1: Identify the vertex

The graph is a parabola opening upwards. The vertex is the minimum point. From the graph, the vertex seems to be at \( x = 2 \) (visually, the lowest point on the parabola is at \( x = 2 \)).

Step2: Determine increasing interval

For a parabola opening upwards (\( a > 0 \) in \( y = ax^2 + bx + c \)), the function is increasing when \( x \) is greater than the \( x \)-coordinate of the vertex. So if the vertex is at \( x = 2 \), the function is increasing for \( x > 2 \), which in interval notation is \( (2, \infty) \).

Answer:

\( (2, \infty) \) (assuming the vertex of the parabola is at \( x = 2 \), the function increases for \( x > 2 \))