Find the vertex and axis and the graph

Question

f(x)=x^2+2x+6

Answer 1

x^2 +2x +6 complete the square

= x^2 +2x + 1 + 5, factor

= (x+1)^2 + 5 is in vertex form (x-h)^2 +k where vertex is (h,k) =(-1,5)

vertex is (-1,5)

It's an upward opening parabola with y intercept = 6 or (0,6)

axis of symmetry is x=-1

a symmetric point on the graph corresponding to the y intercept is (-2,6)

plot those 3 points and draw a smooth parabolic curve through them with minimum point = (-1,5)