Final answer:
To find the time at which an object is at a certain height, set the height equation equal to that height and solve for t using the quadratic formula.
Step-by-step explanation:
The equation h(t)=-16t²+128t+144 represents the height of an object thrown upward from a height of 144 feet with an initial velocity of 128 feet per second. To find the time at which the object is at a certain height, we can set h(t)=-16t²+128t+144 equal to that height and solve for t. This will give us the time in seconds.
For example, if we want to find the time at which h(t)=-16t²+128t+144 is equal to 100 feet, we can solve the equation -16t²+128t+144=100. By rearranging the equation and using the quadratic formula, we can find the values of t that satisfy the equation.