SOLUTION: Write an equation of the form f(x)=ax^2+bx+c in which f(0)= -6 f(2)= -3 and f(4)=2 I found out that c is -6, I tried using the sum and product of roots but I can't figure it out

Question 691732: Write an equation of the form f(x)=ax^2+bx+c in which f(0)= -6 f(2)= -3 and f(4)=2
I found out that c is -6, I tried using the sum and product of roots but I can't figure it out, please help?
Answer by sachi(548) (Show Source): You can put this solution on YOUR website!
f(x)=ax^2+bx+c
f(0)= -6
or a*0+b*0+c=-6
or c=-6 .............1
f(2)= -3
or a*2^2+b*2+c =-3
or 4a+2b-6=-3
or 4a+2b=6-3=3.......2
f(4)=2
a*4^2+b*4+c =2
or 16a+4b-6=2
or 16a+4b=6+2=8
or 4a+b=8/4=2.......3
subtracting eqn 3 from eqn 2
4a+2b=3
4a+b=2
- - -
---------
b=1
putting this in eqn 2
4a+2*1=3
or 4a=3-2=1
or a=1/4
so a=1/4,b=1&c=-6
ans
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