Question

mackenzie launches a toy rocket from a platform. 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.
(graph with points (0, 40), (2.25, 121), (5, 0) and axes labeled height (in feet) and time (in seconds))
answer attempt 1 out of 2
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(options: ∅, or, ∪, ∞, <, >, ≤, ≥, ,, ,), (,, (,)) all real numbers

Explanation:

Step1: Identify the vertex

The graph is a parabola opening downward (since the rocket goes up then down), so the vertex \((2.25, 121)\) is the maximum point.

Step2: Determine the increasing interval

For a downward - opening parabola, the function is increasing to the left of the vertex (in terms of the \(t\) - axis, which is the independent variable here). The rocket starts at \(t = 0\) (point \((0,40)\)) and the vertex is at \(t=2.25\). So the height is increasing when \(t\) is in the interval from \(0\) to \(2.25\) (not including \(2.25\) at the end because at \(t = 2.25\) the function reaches its maximum and then starts to decrease). In interval notation, this is \((0,2.25)\).

Answer:

\((0, 2.25)\)