Question 678237: Write a quadratic function that fits each set of points.
(1,2), (2,-1), and (5,2)
Please, and Thank You :) This is also my last question as I was able to do the rest of them. :)
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Write a quadratic function that fits each set of points.
(1,2), (2,-1), and (5,2)
:
Using the form: ax^2 + bx + c = y, find a, b, c using elimination, 3 equations
x=1,y=2
1^2a + 1b + c = 2
a + b + c = 2
:
x=2, y=-1
2^2a + 2b + c = -1
4a + 2b + c = -1
:
x=5, y=2
5^2a + 5b + c = 2
25a + 5b + c = 2
:
Eliminate c, subtract the 1st equation from the 2nd and 3rd
4a + 2b + c = -1
a + b + c = 2
----------------Subtraction eliminates c
3a + b = -3
:
and using the 3rd equation
25a + 5b + c = 2
a + b + c = 2
----------------Eliminate c again
24a + 4b = 0
:
Multiply 3a+b=-3 by 4 and subtract from the above equation
24a + 4b = 0
12a + 4b = -12
----------------Subtraction eliminates b, find a
12a = 12
a = 1
:
Find b using 3a+b=-3, replace a with 1
3(1) + b = -3
3 + b = -3
b = -3 - 3
b = -6
:
Find c using the 1st original equation
1 - 6 + c =
-5 + b = 2
c = 2 + 5
c = 7
;
The equation: y = x^2 - 6x + 7
:
You can confirm this yourself, replace the given x and see if you get the given y
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