If an object is dropped from a height of 144 feel the function h(t)= -16t^2 +144 gives the height of the object after t seconds. when will the object hit the ground

   In order to solve this problem, you need to solve for t, which is the time the object will hit the ground, such that h(t) =0, due to how that means that you are finding the time it takes for the object to reach the height of the ground, which is most likely assumed from the problem to be 0 ft. Hence, your equation is now 0= -16t^2+144. You should then divide the leading coefficient from both sides of the equation, which is -16, as it is not only negative but also not equal to 1, which is the only circumstance in which you don't have to get rid of it. After that, you will get 0 on one side of the equation because 0 divided by anything but 0 is also equal to 0. The other side of the equation should be t^2 with a leading coefficient of 1 now, whereas that value is added to 144/(-16). You will be left with an answer that is a special case, where each of the terms have square roots and each of the terms are perfect squares. Therefore, you can factor the terms, whereas you have to reject the negative answer that you're left with, because time can't be negative. Your other value, which is your answer, has to be expressed as equivalent to t and with the unit of seconds.