Question 1171725: A parachutist jumps from an altitude of 2000m.
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Time(s) 0 , 3 , 6 , 9 , 12
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Height(m) 2000, 1911 , 1650, 1215 , 608
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Determine the equation for your curve of good fit in factored form y=a(x-r)(x-s)
and using your equation estimate the parachutist's distance from the ground after 10 s.
Thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i used a polynomial regression calculator to get the following results.
1.9999428571428573e+003 = constant term
-7.6190476190475920e-001 = x term
-9.6031746031746028e+000 = x^2 term
this polynomial regression calculator is at https://arachnoid.com/polysolve/
equation is y = -9.6031746031746028*10^0*x^2 - 7.6190476190475920*10^-1*x + 1.9999428571428573*10^3.
i converted the scientific notation to decimal form to get:
y = -9.603174 * x^2 - .761907 * x + 1999.942857
i graphed the equation in decmos.com calculator at https://www.desmos.com/calculator
the graph showed me the zero points at x = -14.392 and x = 14.471 as shown below.
my equation became y = -9.603174 * (x + 14.471) * (x - 14.392).
i checked all the points from the data table.
they were all close.
i then looked for the value of y when x = 10.
the graph showed me that the value of y = 1032.117 when x = 10
that would be the height that the parachutist was at after 10 seconds.
the graph of the value of y when x = 0,3,6,9,12, and 10 are shown below.
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