Hello There!!
I'm not a 100% sure this right.
Explanation:
f(x)=ax2+bx+c for which f(1)=0, f(-2)=6 and f(2)=-14
0 = a +b +c
6 =4a -2b +c
-14=4a+2b +c
subtract third equation from second to get
20 = -4b and so b=-5
first equation is now 5 = a+c
second is now -4=4a+c
subtract to get -9=3a and so a=-3
equation one now is 0=-3-5+c or c=8 Hope This Helps!!