Please help Find a second degree polynomial function, f(x)=ax^2+bx+c where such that f(2)=-8, f'(2)=3, and f''(2)=4

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Please help Find a second degree polynomial function, f(x)=ax^2+bx+c where such that f(2)=-8, f'(2)=3, and f''(2)=4

Mathematics
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hints: f(x) = ax^2 + bx + c f ' (x) = 2ax + b f '' (x) = 2a
The a, b, and c are confusing me
Do you see how I got f ' (x) = 2ax + b and f '' (x) = 2a ??

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\[ f(x)=ax^2+bx+c\\ f'(x)=2ax+b\\ f''(x)=2a \] Given \[ f(2) = 8=4a+2b+c \\ f'(x) =3=4a+b\\ f''(x) =4=2a \Rightarrow a=2\\ \] Solving above equation, we can say: \[ a=2\\ 3 = 4\times 2+b \Rightarrow b=3-8=-5 \\ 4 \times 2+2\times (-5)+c=8 \Rightarrow c = 10 \] Therefore \[a =2 \\ b=-5 \\ c= 10 \]
No direct answers please.
Hi @ospreytriple , what do you mean by no direct answers?
Hi @sgadi . I noticed that you solved the problem for the asker. OpenStudy's code of conduct states that helpers are not to provide answers to askers but to assist and guide them so that they may be able to solve the problems for themselves.
Okay so where did you get the 4 from in f(2)=-8?
@ospreytriple , I understand now. I am sorry. Shall I delete the post?
Hey, I'm not a moderator. Just a heads up for future reference.
@ospreytriple , Thank you. @Sasha.O , Did you get everything clear?

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