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 rocket’s height is increasing. the graph has points (0, 40), (2.25, 121), (5, 0).

Explanation:

Step1: Understand the graph type

The graph of the rocket's height vs. time is a parabola opening downward (since it has a maximum point), which represents a quadratic function. For a quadratic function with a maximum (opening downward), the function is increasing before reaching the vertex and decreasing after.

Step2: Identify the vertex

The vertex of the parabola (the maximum point) is given as \((2.25, 121)\). This means at \(t = 2.25\) seconds, the rocket reaches its maximum height.

Step3: Determine the increasing interval

Before reaching the vertex (i.e., for values of \(t\) less than \(2.25\) seconds, starting from \(t = 0\) when the rocket is launched), the height of the rocket is increasing. So the interval for which the rocket's height is increasing is from \(t = 0\) to \(t = 2.25\), which can be written as \(0 < t < 2.25\) (or in interval notation \((0, 2.25)\)).

Answer:

\(0 < t < 2.25\) (or in interval notation: \((0, 2.25)\))