I've tried to figure it out by substituting the x and y values into an equation (y=ax2+bx+c) and writing a system of equations, but I got confused.
You have three unknowns: a, b, and c, as parabola coefficients. You have three points, which lie on the parabola. Plug in their coordinates to obtain three equations containing a,b, and c.
1) point (2,20)
2) point (-2, -4)
3) point (0,8)
So the final system looks as follows:
Since c is determined by the third equation already, plug its value into the first and the second equation.
Add two equations together, to obtain 8a=0; a=0; then 2b=12 or b=6.
Answer: a=0; b=6; c=8
Equation of parabola: y=6x+8.
So parabola in your case is degenerate and all three points lie on a straight line.