Find the quadratic function f(x)=ax^2+bx+c for which f(1)=0, f(-2)=6 and f(2)=-14

Question

find the quadratic function f(x)=ax^2+bx+c for which f(1)=0, f(-2)=6 and f(2)=-14

Answer 1

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