Question

a rocket is launched in the air. the graph below shows the height of the rocket h in feet after t seconds. find the interval for which the rockets height is increasing.

Explanation:

Step1: Analyze the graph

The graph is a parabola opening downwards. The vertex is at \((25, 10000)\).

Step2: Determine the increasing interval

For a parabola opening downwards \(y = ax^{2}+bx + c\) (\(a<0\)), the function is increasing on the interval \((-\infty,x - coordinate\ of\ vertex)\). In the context of \(t\) (time), since the vertex occurs at \(t = 25\), the rocket's height is increasing when \(t\) is in the interval from \(t=0\) to \(t = 25\).

Answer:

The rocket's height is increasing on the interval \((0,25)\)