Question

NASA's KC135A aircraft flies in parabolic arcs to simulate the weightless experienced by astronauts in space. The height h of the aircraft (in feet) t seconds after it begins its parabolic flight can be modeled by the equation h(t) = -9.09(t-32.5)^2+34000. What is the maximum hight of the aircraft during this maneuver and when does it occur?

Answer 1

34,000 feet at 65/2=32.5 seconds

Answer 2

explain how you got that please

Answer 3

Well if you look at the equation, you'll see that any number besides 32.5 will multiply -9.09 by a positive number (since its squared first). When you multiply a negative and a positive you get a negative which is then added to 34000. So in order to maximize the final value you want -9.09 multiplied by zero so nothings subtracted from 34000.
So the max value is 34000 and x must be 32.5 to achieve that.
Satisfactory?