In y=ax²+bx+c, the vertex is when x=-b/(2a), the x intercept is the value of x when y=0, and the y intercept is the value of y when x=0 in this case, a=-1, b=2, so the vertex is when x=-2/[2*(-1)]=1 when x=1, y=-(1)²+2*1+1=2, so the vertex is (1,2)
when x=0, y=1, the x intercept is (0,1) when y=0, -x²+2x+1=0, use the quadratic formula to find x: x=-1+√2, x=-1-√2 so the symmetry point the the y intercept is (-1+√2, 0) (-1-√2, 0)