Question

The following table represents a quadratic function.

Answer 1

The following are true:
The graph has a relative minimum
The graph of the quadratic function has a vertex at (0,5) 
The graph opens up
The axis of symmetry is x=0

It has a minimum point; there is a smallest value of y for this function.  The vertex will be that minimum point, (0, 5).  Since that is the vertex, that means x=0 is the axis of symmetry.  It opens up because all of the other points are above the vertex.

It does not have any x-intercepts, since the lowest y-value is 5 (the vertex).  The y-intercept would be at (0, 5), not (5, 0).