Answer:
The axis of symmetry is at 
The graph has an x-intercept at 
The graph has a vertex at 
Step-by-step explanation:
we have

Statements
case 1) The graph has root at
and 
The statement is False
Because, the roots of the quadratic equation are the values of x when the value of y is equal to zero (x-intercepts)
Observing the graph, the roots are at
and 
case 2) The axis of symmetry is at 
The statement is True
Observing the graph, the vertex is the point 
The axis of symmetry in a vertical parabola is equal to the x-coordinate of the vertex
so
the equation of the axis of symmetry is 
case 3) The graph has an x-intercept at 
The statement is True
see procedure case 1)
case 4) The graph has an y-intercept at 
The statement is False
Because, the y-intercept is the value of y when the value of x is equal to zero
Observing the graph, the y-intercept is the point 
case 5) The graph has a relative minimum at 
The statement is False
Because, is a vertical parabola open downward, therefore the vertex is a maximum
The point
represent the vertex of the parabola, so is a maximum
case 6) The graph has a vertex at 
The statement is True
see the procedure case 5)
see the attached figure to better understand the problem