axis of symmetry is also the x coordinate of the vertex
if you have
f(x)=ax^2+bx+c
vertex x coordinate is
-b/2a
a=1
b=4
-4/2(1)=-4/2=-2
x coordinate of vertex=-2 aka axis of symmmetry
find y coordinate
input -2 for x
y=(-2)^2+4(-2)-5
y=4-8-5
y=-9
axis of symmetry is x=-2
vertex is (-2,-9)