Question

christopher kicks a football. the graph below shows the height of the football h in meters after t seconds. find the interval for which the footballs height is increasing.

Explanation:

Step1: Analyze the graph

A function \(y = f(x)\) is increasing when as \(x\) increases, \(y\) also increases. In the context of the height - time graph (\(h(t)\)), we look at the behavior of the curve.

Step2: Identify the increasing interval

Looking at the given graph of \(h(t)\) (a parabola opening downwards with vertex at \((1,4.9)\)), for \(t\) values from \(t = 0\) to \(t=1\), as \(t\) (time) increases, \(h\) (height) increases.

Answer:

The interval for which the football's height is increasing is \(0\lt t\lt1\)