Question

Determinati functia de gradul al doilea al carei grafic contine punctele A(0,0), B(2,2), C (-1,2)

Answer 1

$f(x)=a x^{2} +bx+c \\ f(0)=0;c=0 \\ f(2)=2;4a+2b=2 \\ f(-1)=2;a-b=2$
rezolvind sistemul obtinem
$\left \{ {{4a+2b=2} \atop {a-b=2}} \right. \\ \left \{ {{6a=6} \atop {b=-1}} \right. \\ \left \{ {{a=1} \atop {b=-1}} \right.$
deci functia cautata este
$f(x)= x^{2} -x$