I've tried to figure it out by substituting the x and y values into an equation (y=ax^{2}+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)
a*2^{2}+b*2+c=20 or
4a+2b+c=20
2) point (-2, -4)
a*(-2)^{2}-2b+c=-4 or
4a-2b+c=-4
3) point (0,8)
a*0^{2}+b*0+c=8 or
c=8
So the final system looks as follows:
4a+2b+c=20
4a-2b+c=-4
c=8
Since c is determined by the third equation already, plug its value into the first and the second equation.
We obtain:
4a+2b+8=20
4a-2b+8=-4
4a+2b=12
4a-2b=-12
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.