I need help solving this one problem assigned for homework in my Algebra II HOnors class.

Let f(x)=ax^2+bx+c such that

f(0)=f(1)

f(2)=2f(1)

f(3)=16

Calculate f(-1)

I'm lost, and have no idea where to start. All I've been able to work out is that -a=b because

f(0)=f(1)

f(0)=a(0)^2+b(0)+c

f(0)=c

f(1)=a(1)^2+b(1)+c

f(1)=a+b+c

a+b+c=c

a+b=0

-a=b

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