Question

wyatt throws a ball up in the air. the graph below shows the height of the ball h in feet after t seconds. find the interval for which the balls 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 slope of the graph.

For a parabola (which is a quadratic function \(h(t)=at^{2}+bt + c,a
eq0\)), if \(a<0\), the parabola opens downwards. The vertex of the parabola \(t =-\frac{b}{2a}\) is the maximum point.

Before the vertex, the function is increasing.

Step2: Determine the interval

The vertex of the parabola (the maximum point of the height - time graph) is at \(t = 0.75\) seconds.

Since the ball starts at \(t = 0\) seconds, and the function \(h(t)\) (height as a function of time) is increasing from \(t=0\) until it reaches the vertex at \(t = 0.75\) seconds.

Answer:

The ball's height is increasing on the interval \(0