Well there are numerous ways to solve this but I'll tell you the shortest one (at least according to me).
When you see a parabola of form
y
=
a
x
2
+
b
x
+
c
the slope of its vertex is 0. We know that the formula of the slope of any instantaneous line is
d
y
d
x
so
d
2
x
2
+
8
x
+
5
d
x
=
0
On solving this we get
x
=
−
2
Put this in our original equation of parabola and
y
=
−
3
This coordinates of the vertex are (-2,-3)
