y=ax^2+bx+c
when x=-2, y=1: 1=4a-2b+c
when x=0, y=1: 0x^2+0b+c=1 =>c=1
when x=1, y=4: 1a+1b+c=4, because c=1, a+b=3
back to x==-2, y=1, plugc=1 in the equation, 4a-2b=0
solve the system equation: a+b=3
4a-2b=0
a=1, b=2
so the quadratic equation is: x^2+2x+1=0
