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
The scenario relates to the speed of a car (x) and the braking distance at that speed (y). So presumably another coordinate can also be 0,0.
Given the staring coordinate of 0,0 I have worked out that in the formula form y = ax^2 + bx + c that c = 0, but I cannot work out the procedure to use to solve for a and b and come up with the equation. I have tried simultaneous equations but think I am doing something wrong. My boyfriend talked about solving it by taking logs but we have not been taught that way at school.
Thanks
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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
------------
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
=======================================
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
------------------------------------
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
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