Table below shows height, in feet, of a rocket about the ground t seconds after being launched.
Quadratic best-fit model, how long after the rocket wasw launched was it 100 feet above teh ground?
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Given the following points find the best-fit quadratic model:
(1,211),(2,215),(4,127), and (5,35).
We can use technology or solve the following system of equations:
a + b + c = 211
4a + 2b +c = 215
16a +4b +c = 127
Solving the system yields a=-16,b=52 and c=175.
So a model that fits the points is `h=-16t^2+52t+175`
**Check: if t=5 `h=-16(5)^2+52(5)+175=35` **
Then we need to find the time(s) when the rocket is at 100ft.
`-16t^2+52t+175=100 ==> -16t^2+52t+75=0`
We can use the quadratic formula to solve:
`t~~(-52+86.63)/(-32)` or `t~~(-52-86.63)/(-32)` so
`t~~-1.08` or `t~~4.33` The first answer implies a time before launch, so the time that the rocket hits 100 ft is approximately 4.33 seconds after launch.
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