SOLUTION: Find the quadratic Equation that fits the following set of Data points. (5,162),(4,110),(1,14)

Question 1150290: Find the quadratic Equation that fits the following set of Data points. (5,162),(4,110),(1,14)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find the quadratic Equation that fits the following set of Data points. (5,162),(4,110),(1,14)
:
using the form: ax^2 + bx + c = y
x=5, y=162
25a + 5b + c = 162
:
x=4; y=110
16a + 4b + c = 110
:
x=1, y=14
a + b + c = 14
:
use elimination on 1st two equations
25a + 5b + c = 162
16a + 4b + c = 110
--------------------subtraction eliminates c
9a + b = 52
:
use elimination on last two equations
16a + 4b + c = 110
a + b + c = 14
--------------------subtraction eliminates c
15a + 3b = 96
simplify divide by 3
5a + b = 32
:
use elimination on the resulting two equations
9a + b = 52
5a + b = 32
--------------subtraction eliminates b
4a = 20
a = 5
:
substituting 5 for a in the 1st two equations
125 + 5b + c = 162
5b + c = 162 - 125
5b + c = 37
and
80 + 4b + c = 110
4b + c = 110 - 80
4b + c = 30
:
using elimination in these two equations
5b + c = 37
4b + c = 30
-------------subtraction eliminates c
b = 7
:
use the last original equation to find c
5 + 7 + c = 14
c = 14 - 12
c = 2
:
The equation for the given points:
y = 5x^2 + 7x + 2
:
:
I'll let you confirm this is true
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