Answer:
<u>Part (a)</u>
It depends how your calculator calculates quadratic regressions.
For my calculator:
- Go to Statistics menu
- Select quadratic regression: y=a+bx+cx²
- Input the x and y values from the given table
- Go to options and select regression calc
a = 1.177142857 = 1.18 (nearest hundredth)
b = 42.22257143 = 42.22 (nearest hundredth)
c = -12.87142857 = -12.87 (nearest hundredth)
⇒ y = 1.18 + 42.22x - 12.87x²
Therefore, the quadratic regression equation in standard form is:
<u>Part (b)</u>
To estimate the height of the rocket after 5 seconds, input x = 5 into the regression equation:
As this gives us a negative value, this means that the rocket would have come back to the ground before 5 s. Therefore, the height of the rocket at 5 s will be 0 ft.
(see attached graph → the rocket will hit the ground at approx 3.3 s)
