Question

Which is the graph of the function f(x) = x2 + 2x + 3?

Answer 1

dy/dx=2x+2

So velocity will be zero when 2x+2=0, x=-1

Since d2y/dx2=2, it has a constant positive acceleration of 2, so that when dy/dx=0 it is at an absolute minimum value for f(x), which is also the vertex.

y(-1)=1-2+3=2

So the vertex is at (-1,2), which is an absolute minimum so the parabola opens upwards.

And by symmetry we can say that f(0)=f(-2)=3 so you have another two points that you can see (-2,3) and (0,3)

Answer 2

its the first answer on e2020 :D