Question

genesis throws a ball up in the air. the graph below shows the height of the ball h in meters after t seconds. find the interval for which the balls height is decreasing.

Explanation:

Step1: Identify the vertex

The graph is a parabola (since the motion of a ball thrown upward is a quadratic function), and the vertex is at \( (1.5, 11.025) \). The vertex of a parabola represents the maximum (or minimum) point. For a parabola opening downward (which this is, since the ball goes up and then down), the function is increasing before the vertex and decreasing after the vertex.

Step2: Determine the decreasing interval

The ball hits the ground at \( t = 3 \) (from the point \( (3, 0) \)). So, after the vertex at \( t = 1.5 \), the height starts to decrease until the ball hits the ground at \( t = 3 \). Therefore, the interval where the height is decreasing is when \( t \) is between \( 1.5 \) and \( 3 \), which is \( (1.5, 3) \) (or \( 1.5 < t < 3 \)).

Answer:

\( (1.5, 3) \) (or in interval notation, \( 1.5 < t < 3 \))