SOLUTION: Find a quadratic function that fits the set of data points: (1,4),(-1,-2),(2,13)

Question 192159: Find a quadratic function that fits the set of data points:
(1,4),(-1,-2),(2,13)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find a quadratic function that fits the set of data points:
(1,4),(-1,-2),(2,13)
:
Using the form ax^2 + bx + c = y; we can use elimination here
:
Eq1; x=1, y=4
(1^2)a + 1b + c = 4
1a + 1b + c = 4
:
Eq2; -1, -2
+1a - 1b + c = -2
;
Eq3; 2, 13
4a + 2b + c = 13
:
Subtract the 2nd equation from the 1st
1a + 1b + c = 4
1a - 1b + c = -2
--------------------Subtraction eliminate a & c
2b = 6
b = 3
:
Substitute 3 for b in the 1st equation:
a + 3 + c = 4
a + c = 4 -3
a + c = 1
;
do the same with the 3rd equation
4a + 2(3) + c = 13
4a + 6 + c = 13
4a + c = 13 - 6
4a + c = 7
:
Substract a + c = 1 from the above equation:
4a + c = 7
1a + c = 1
-------------subtraction eliminate c, find a
3a = 6
a = 2
;
Using a = 2 in 4a + c = 7
4(2) + c = 7
8 + c = 7
c = 7 - 8
c = -1
:
the quadratic equation that satisfies these points: y = 2x^2 + 3x - 1
:
You can prove this to yourself by substituting for x and finding y for each point
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