Final answer:
To find the time it takes for the rocket to reach a height of 1,304 feet, solve the quadratic equation -16t^2 + 288t - 1296 = 0. Use the quadratic formula to calculate the two possible solutions for t and select the positive solution.
Step-by-step explanation:
To find the time it takes for the rocket to reach a height of 1,304 feet, we need to solve the equation h = -16t^2 + 288t + 8, where h is the height and t is the time in seconds.
Set h to 1,304 and solve for t: 1304 = -16t^2 + 288t + 8. Rearrange the equation to form a quadratic equation: -16t^2 + 288t - 1296 = 0.
Use the quadratic formula to solve for t: t = (-b ± √(b^2 - 4ac)) / (2a). In this case, a = -16, b = 288, and c = -1296. Substitute these values into the formula and calculate the two possible solutions for t. The positive solution is the time it takes for the rocket to reach a height of 1,304 feet.