The function's vertex is found at the function's highest or lowest point.
In this case it's the lowest point and can be read as (-2,-4).
For quadratic functions, the axis of symmetry always goes through the vertex. Read the x-coordinate of the vertex and you'll find the axis of symmetry.
The x-coordinate is -2 so the axis of symmetry is x=-2.
The function's zeros is where the value of the function is 0, so the x-values when the curve intersects the x-axis.
The zeros are x=-5 and x=1.