Question 128294: At an airshow, a plane is in a power dive. The height of the plane, in metres above the ground , is recorded for the first six seconds.
Time(s): 1,2,3,4,5,6
Height(m): 214,180,150,124,102,84
a) Algebraically determine the quadratic function that models the path followed by the plane. Express the function in the form y=ax^2+bx+c.
b) Use the function to determine the minimum height of the plane.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! At an airshow, a plane is in a power dive. The height of the plane, in metres above the ground , is recorded for the first six seconds.
Time(s): 1,2,3,4,5,6
Height(m): 214,180,150,124,102,84
a) Algebraically determine the quadratic function that models the path followed by the plane. Express the function in the form y=ax^2+bx+c.
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Substitute three x/y pairs into the form to get three equations
with variables a,b, and c.
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f(1) = a + b + c = 214
f(2) =4a + 2b + c = 180
f(3) =9a + 3b + c = 150
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I used the Matrix function of a TI calculator to find the following:
a = 2
b = -40
c = 252
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EQUATION:
y = 2x^2-40x+252
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b) Use the function to determine the minimum height of the plane.
minimum occurs at x = -b/2a = 40/4 = 10
f(10) = 52
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At 10 seconds the plane will be at 52 ft.
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Cheers,
Stan H.
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