Answer:
y = 2x^2 -x -3
Explanation:
It can be convenient to use the quadratic regression capability of a graphing calculator or spreadsheet. That's what we did in the attachment.
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Fill in the given points in the equation to find three linear equations in a, b, c.
3 = a(2^2) +b(2) +c
7 = a(-2)^2 +b(-2) +c
-2 = a(1^2) +b(1) +c
Subtracting the last equation from the first two gives ...
(3) -(-2) = (4a +2b +c) -(a +b +c) ⇒ 5 = 3a +b
(7) -(-2) = (4a -2b +c) -(a +b +c) ⇒ 9 = 3a -3b . . . . . [eq5]
Subtracting the second of these equations from the first gives ...
(5) -(9) = (3a +b) -(3a -3b) ⇒ -4 = 4b
b = -1
Dividing [eq5] by 3 gives ...
3 = a - b
3 = a -(-1)
2 = a
Using the original 3rd equation, we have ...
-2 = a +b +c
-2 = 2 +(-1) + c
-3 = c . . . . . . . . subtract 1
The desired quadratic is ...
y = 2x^2 -x -3