Question

Cho hàm số \(y=f\left(x\right)=ax^2+bx+c\) . Tính \(f\left(-2\right)\) Cho biết \(f\left(0\right)=2014\) ; \(f\left(1\right)=2015\) ; \(f\left(-1\right)=2017\) .

Answer 1

\(\left\{{}\begin{matrix}f\left(0\right)=2014\Rightarrow c=2014\left(1\right)\\f\left(1\right)=2015\Rightarrow a+b+c=2015\left(2\right)\\f\left(-1\right)=2017\Rightarrow a-b+c=2017\left(3\right)\end{matrix}\right.\)

\(f\left(-2\right)=4a-2b+c\)

Lấy (3) nhân 3 công (2) trừ (1) nhân 2

\(f\left(-2\right)=4a-2b+c=3.2017+2015-3.2014\)

\(f\left(-2\right)=3\left(2017-2014\right)+2015=2024\)