Question 190141
I need to find the equation that goes with a series of plotted points. The points form what appears to be part of a parabola. The coordinates given are: 
x y
32 6
48 14
64 24
80 38
96 55
112 75 
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You are thinking right.
Use any three of the points to generate 3 equations in a,b,c
Then solve the system for a,b,c.
6 = a(6^2) + b(6) + c
14= a(48^2) + b(48) + c
24= a(64^2) + 64b + c
----------------------------
I used a matrix method to solve the system and found:
a = 0.00749
b = -0.21408
c = 7.01478
---------------
Equation:
y= 0.00749x^2 - 0.21408x + 7.01478
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I also ran a Quadratic Regression program against
the whose set of data and came up with:
y = 0.006x^2-0.2321x+0.6
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The fact that these answers are not the same means
that not all the points lie exactly on a parabola.
That may be what your instructor is trying to show.
===================================================

Cheers,
Stan H. 







need to find the equation that goes with a series of plotted points. The points form what appears to be part of a parabola. The coordinates given are: 
x y
32 6
48 14
64 24
80 38
96 55
112 75