Ok, the line will cut the y axis where x=0.
Substitute x=0 into the equation, and you get y=-2. So point of interception is at:
Now, the line will cut the x axis where y=0. To find this, we can try to factorise:
x=-2 and x=-1/4
x intercepts are
Parabolas are symmetrical, so if you take the x intercepts, the line of symmetry will be halfway between them.
(wow, nasty numbers)
x=-1.125 is the line of symmetry.
A question about the vertex: Have you covered differentiation?