Find the equation of the parabola $f(x)=a{x}^2+bx+c$ 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 $\boxed{{\displaystyle -2x^2+3x-6}}$