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

Question

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

jim_thompson5910 · Answer

hints:

f(x) = ax^2 + bx + c
f ' (x) = 2ax + b
f '' (x) = 2a

anonymous · Answer

The a, b, and c are confusing me

jim_thompson5910 · Answer

Do you see how I got f ' (x) = 2ax + b and f '' (x) = 2a ??

sgadi · Answer

$$
f(x)=ax^2+bx+c\
f'(x)=2ax+b\
f''(x)=2a
$$

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 · Answer

No direct answers please.

sgadi · Answer

Hi @ospreytriple , what do you mean by no direct answers?

anonymous · Answer

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 · Answer

Okay so where did you get the 4 from in f(2)=-8?

sgadi · Answer

@ospreytriple , I understand now. I am sorry. Shall I delete the post?

anonymous · Answer

Hey, I'm not a moderator. Just a heads up for future reference.

sgadi · Answer

@ospreytriple , Thank you.

@Sasha.O , Did you get everything clear?