Given 3 points
A= (-1,2)
B= (0,-1)
C= (2,5)
Find ax^2 + bx + c
Then write ax^2 + bx + c = y
Replace (x,y)= (-1,2)
a•(-1^2) + b(-1) + c = 2
a - b + c = 2
Replace (x,y) = (0,-1)
a•0 + b•0 +c = -1
c=-1
Replace (x,y)= (2,5)
a•(2^2) + b•(2) + c = 5
4a + 2b + c = 5
Now organize ,this 3 results
a - b + c = 2
c=-1
4a + 2b + c = 5
Replace c=-1, and solve this 2x2 system
a - b = 2- c = 2-(-1) = 3
4a + 2b = 5 - c = 5-(-1) = 6
And now solve 2x2 system
a - b = 3 (multiply x2)
2a- 2b = 6
4a +2b= 6
Now add both equations
6a + 0 = 12
a= 12/6 = 2
Now find b
b = a - 3 = -1
THEN, NOW finally we have 3 values a,b,c
a= 2. b=-1,. c= -1
Therefore, quadratic equation searched is
y = 2x^2 -x - 1
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