anonymous
  • anonymous
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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SOLVED
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jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
hints: f(x) = ax^2 + bx + c f ' (x) = 2ax + b f '' (x) = 2a
anonymous
  • anonymous
The a, b, and c are confusing me
jim_thompson5910
  • jim_thompson5910
Do you see how I got f ' (x) = 2ax + b and f '' (x) = 2a ??

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sgadi
  • sgadi
\[ f(x)=ax^2+bx+c\\ f'(x)=2ax+b\\ f''(x)=2a \] 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 \[a =2 \\ b=-5 \\ c= 10 \]
anonymous
  • anonymous
No direct answers please.
sgadi
  • sgadi
Hi @ospreytriple , what do you mean by no direct answers?
anonymous
  • anonymous
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.
anonymous
  • anonymous
Okay so where did you get the 4 from in f(2)=-8?
sgadi
  • sgadi
@ospreytriple , I understand now. I am sorry. Shall I delete the post?
anonymous
  • anonymous
Hey, I'm not a moderator. Just a heads up for future reference.
sgadi
  • sgadi
@ospreytriple , Thank you. @Sasha.O , Did you get everything clear?

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