Table below shows height, in feet, of a rocket about the ground t seconds after being launched.   t          h 1         211 2         215 4         127 5           35...

Table below shows height, in feet, of a rocket about the ground t seconds after being launched.  

t          h

1         211

2         215

4         127

5           35

Quadratic best-fit model, how long after the rocket wasw launched was it 100 feet above teh ground?

Asked on by mpumpkin

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

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+-sqrt(52^2-(4)(-16)(75)))/(2(-16))`

`t=(-52+-sqrt(7504))/(-32)`

`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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