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Question
The function $h(t)=-16 t^{2}+48 t+28$ models the height (in feet) of a ball where $t$ is the time (in seconds).
What is the maximum height that the ball reaches? Just write the numerical answer-do not include $h=$ or any units in your answer.
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Answer
The maximum height that the ball reaches is \(\boxed{64}\).
Step 1 ：The function given is a quadratic function. The maximum height of the ball is the maximum value of the function, which occurs at the vertex of the parabola.
Step 2 ：The x-coordinate of the vertex of a parabola given by the equation \(y = ax^2 + bx + c\) is \(-b/2a\).
Step 3 ：In this case, \(a = -16\) and \(b = 48\), so the time at which the maximum height is reached is \(-b/2a = -48/(-32) = 1.5\) seconds.
Step 4 ：We can substitute this value into the function to find the maximum height.
Step 5 ：The maximum height that the ball reaches is \(\boxed{64}\).
