Question

Cho hàm số y = f(x) = ax² + bx + c

Biết f(0) = 2014 ; f(1) = 2015 ; f(-1) = 2017 . Tính f(-2)

Answer 1

Ta có :

\(f\left(x\right)=ax^2+bx+c\)

+) \(f\left(0\right)=2014\)

\(\Leftrightarrow a.0^2+b.0+c=2014\)

\(\Leftrightarrow c=2014\)

+) \(f\left(1\right)=2015\)

\(\Leftrightarrow a.1^2+b.1+c=2015\)

\(\Leftrightarrow a+b+2014=2015\)

\(\Leftrightarrow a+b=1\left(1\right)\)

+) \(f\left(-1\right)=2017\)

\(\Leftrightarrow a.\left(-1\right)^2+b\left(-1\right)+c=2017\)

\(\Leftrightarrow a-b+2014=2017\)

\(\Leftrightarrow a-b=3\left(2\right)\)

Từ \(\left(1\right)+\left(2\right)\Rightarrow\left(a+b\right)+\left(a-b\right)=1+3\)

\(\Leftrightarrow2a=4\)

\(\Leftrightarrow a=2\)

\(\Leftrightarrow b=0\)

Vậy \(f\left(x\right)=2x^2+2014\)

\(\Leftrightarrow f\left(2\right)=2.2^2+2014=2022\)