a,
$M\in (P)\Rightarrow c=-2$ (1)
$N\in (P)\Rightarrow -2.2^2+2b+c=0$ (2)
$(1)(2)\Rightarrow b=5$
Vậy $y=-2x^2+5x-2$
b,
$I\in (P)\Rightarrow -2.1+b+c=3\Leftrightarrow b+c=5$ (1)
$x_{\max}=\dfrac{-b}{2.(-2)}=1\Rightarrow b=4$ (2)
$(1)(2)\Rightarrow c=1$
Vậy $y=-2x^2+4x+1$
c,
$A\in (P)\Rightarrow -2.2^2+2b+c=-3$ (1)
$x_{\max}=\dfrac{-b}{-2.2}=3\Leftrightarrow b=12$ (2)
$(1)(2)\Rightarrow b=12; c=-19$
Vậy $y=-2x^2+12x-19$
d,
$x_{\max}=\dfrac{-b}{-2.2}=2\Rightarrow b=8$ (1)
$(2;0)\in (P)\Rightarrow -2.2^2+2b+c=0$ (2)
$(1)(2)\Rightarrow b=8; c=-8$
Vậy $y=-2x^2+8x-8$