the \hang time\ of a football is the amount o...

# Explanation: ## Step1: Identify function type Since for each value of \(t\) (input - time), there is exactly one value of \(h\) (output - height), it is a one - to - one function. In the context of height over time for a projectile, it is a quadratic function (a parabola opening downwards). ## Step2: Find hang time The hang time is the time when the football hits the ground again. Looking at the graph, if the graph starts at \(t = 0\) and touches the \(t\) - axis again at \(t=3\), the hang time is 3 seconds. ## Step3: Find time of maximum height The maximum of a parabola occurs at its vertex. By observing the graph, the \(t\) - value at the vertex is \(t = 1.5\) seconds. ## Step4: Find maximum height By looking at the \(h\) - value at \(t = 1.5\) on the graph, the maximum height is about 11 meters. ## Step5: Analyze height change For \(t\) between \(t = 0\) and \(t=1.5\), as \(t\) increases, the height \(h\) of the football is increasing. # Answer: - This is the graph of a quadratic function. - The hang time of the football is 3 second(s). - The football reaches its maximum height when \(t = 1.5\) second(s). - The maximum height is about 11 meter(s). - For \(t\) between \(t = 0\) and \(t = 1.5\), the height is increasing.