Question 456616: Please please help
Find the quadraic equation that fits the following set of data points
(5,9),(4,-45),(-1,-15)
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
(5,9),(4,-45),(-1,-15)
:
Using the form: a^2 + b^2 + c^2 = y, write an equation for each ordered pair
:
5,9
5^2a + 5b + c = 9
25a + 5a + c = 9
:
4,-45
16a + 4b + c = -45
:
-1,-15
1a - 1b + c = -15
:
You can solve this as a 3X4 matrix
25 5 1 9
16 4 1 -45
1 -1 1 -15
:
but you can also use elimination/substitution, which will take longer
:
Subtract the 2nd equation from the 1st equation
25a + 5b + c = 9
16a + 4b + c = -45
------------------------eliminates c
9a + b = 54
for substitution
b = (54-9a)
:
Subtract the 3rd equation from the 1st equation
25a + 5b + c = 9
1a - 1b + c = -15
------------------------eliminates c again
24a + 6b = 24
Replace b with (54-9a)
24a + 6(54-9a) = 24
24a + 324 - 54a = 24
24a - 54a = 24 - 324
-30a = -300
a = +10
find b
b = 54 - 9(10)
b = 54 - 90
b = -36
:
Use the 1st equation to find c
25(10) + 5(-36) + c = 9
250 - 180 + c = 9
70 + c = 9
c = 9 - 70
c = -61
:
The equation for these ordered pairs, y = 10x^2 - 36x - 61
:
I confirmed this using the matrix feature on my calc.
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