Question 737563
Write each question in standard form. Identify the vertex, axis of symmetry and direction of opening of the parabola. 
y=x^2+2x+2
complete the square:
y=(x^2+2x+1)-1+2
{{{y=(x+1)^2+1}}}
This is an equation of a parabola that opens upward.
Its standard form of equation: {{{y=A(x-h)^2+k}}}, (h,k)=(x,y) coordinates of the vertex, A is a coefficient that affects the slope or steepness of the curve.
..
For given parabola:
vertex: (-1,1)
axis of symmetry: x=-1
parabola opens upward.

see graph below as a visual check:
{{{ graph( 300, 300, -10, 10, -10, 10, (x+1)^2+1) }}}