What is the equation for this parabola (located above) in vertex form?

Answer:
f(x)=x²-2x-2
Step-by-step explanation:
f(x)=ax²+bx+c
f(0)=-2 => c= -2
f(1)= -3=> a+b-2=-3; a+b=-1
f(2)= -2; 4a+2b-2=-2; 4a+2b=0; 2a+b=0
a+b=-1 and 2a+b=0
2a+b-(a+b)=0+1=> a=1
2+b=0=> b=-2
f(x)=x²-2x-2