Find the equation of the parabola $f(x)=a x^{2}+b x+c$ that passes through the three points $(-3,-33),(0,-6)$, and $(2,-8)$

Step 1 ：Plug in the given points into the equation to create a system of linear equations:

Step 2 ：1. \(9a - 3b + c = -33\)

Step 3 ：2. \(c = -6\)

Step 4 ：3. \(4a + 2b + c = -8\)

Step 5 ：Solve the system of linear equations for a, b, and c:

Step 6 ：From equation 2, we have \(c = -6\)

Step 7 ：Substitute \(c = -6\) into equations 1 and 3:

Step 8 ：1. \(9a - 3b - 6 = -33\)

Step 9 ：3. \(4a + 2b - 6 = -8\)

Step 10 ：Solve equations 1 and 3 for a and b:

Step 11 ：\(a = -2\) and \(b = 3\)

Step 12 ：Final Answer: The equation of the parabola is \(\boxed{-2x^2 + 3x - 6}\)