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 $f(x) = -2x^2 + 3x -1$