Question

Determinati functia polinomiala de gradul 2, f(x)= ax^2+bx+c care verifica reletiile : f(2)=9 , f derivat(1)= 2, f derivat de doua ori (0)= 8. ajutooor , e urgent

Answer 1

f(x)=ax^2+bx+c
f'(x)=2ax+b
f"(x)=2a
f(2)=4a+2b+c=>16-12+c=9=>c=5
f'(1)=2a+b=2=>b=-6
f"(0)=2a=8=>a=4
=>f(x)=4x^2-6x+5

Answer 2

f(x) = ax^2+bx+c

f''(x) =  (2ax+b)' = 2a
f''(0) = 8 => 2a = 8 => a = 4

f'(x) = 2ax+b = 2·4x+b = 8x+b
f'(1) = 2 => 8+b = 2 => b = -6

f(x) = ax^2+bx+c = 4x^2-6x+c 
f(2) = 9 => 4·4-6·2+c =9 =>16-12+c = 9 => c = 5

=> f(x) = 4x^2-6x+5