Parabola by the points

Problem:

Solution:

We knew that

$ a(1)^2 + b(1) + c = 0 $
$ a(-1)^2 + b(-1) + c = -6 $


$ a(2)^2 + b(2) + c =-3 $

 Simplifying them, we get

$ a + b + c = 0 $
$ a - b + c = -6 $
$ 4a + 2b + c = -3 $

Subtracting the 1st equation by the 2nd equation, we get $ 2b = 6 $ or $ b = 3 $.
Substitute this result back to the equation 1 get $ a + c = -3 $.
Substitute this result to the equation 3 get $ 4a + 6 + c = -3 $, subtracting this with the equation above, we get $ 3a + 6 = 0 $, therefore $ a = -2 $

Last but not least substitute the two results back to equation 1, we finally get $ c = -1 $.

Therefore the equation is $ f(x) = -2x^2 + 3x -1 $