A firecracker is fired straight up into the air out of a window of a building. Its height, in feet, is given by
h - 16t² + 96t + 112, where t is the time, in seconds, the fircracker has been in the air.
At some point in its path it reaches a highest point.

Step-by-step explanation:I assume our task is to find that point of time, when it reaches the highest point.and the function ish(t) = -16t² + 96t + 112well, a maximum or minimum of a curve (function) is found as a zero solution of the first derivative of the function.given the nature of the function, the extreme point has to be a maximum (the firecracker goes up and then down again).h'(t) = -32t + 96we are looking for the zero :0 = -32t + 9632t = 96t = 3 seconds so, after 3 seconds, the firecracker reaches its highest point, which is at-16×3² + 96×3 + 112 = -16×9 + 96×3 + 112 = = -144 + 288 + 112 = 256 ftFYI - we know for x = 0 (the starting point) the height of the starting window was 112 ft.