Diketahui:

$a\ =\left(-1,0\right)$

$b\ =\left(0,-2\right)$

$c\ =\left(1,-5\right)$

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

Ditanya:

Nilai $a$?

Jawab:

$a=\left(-1,0\right)$

$\Leftrightarrow0=a-b+c$ $...$ (1)

$b=\left(0,-2\right)$

$\Leftrightarrow-2=c$ $$ $...$ (2)

$c\left(1,-5\right)$

$\Leftrightarrow-5=a+b+c$ $$ $...$ (3)

Substitusi persamaan (2) ke persamaan (3)

$\Leftrightarrow-5=a+b-2$

$\Leftrightarrow-3=a+b$ $...$ (4)

Substitusi persamaan (2) ke persamaan (1)

$\Leftrightarrow2=a-b$ $...$ (5)

Eliminasi (4)+(5)

$\Leftrightarrow-1=2a$ $$

$\Leftrightarrow a=-\frac{1}{2}$

Jadi, Nilai $a$ adalah $-\frac{1}{2}$