Step-by-step explanation:
We must take our equation and put it in vertex form,
f
(
x
)
=
a
(
x
−
h
)
2
+
k
where
h
,
k
is our vertex.
This equation will not factor into two squares
(
x
−
h
)
2
so we must use the completing the square method.
First we'll get rid of the
3
by subtracting it giving
x
2
−
4
x
=
−
3
Next we take half of the -4 the square it and add it to our equation to give us
x
2
−
4
x
+
4
. Since we added
4
to the left, we must also add it to the right giving
x
2
−
4
x
+
4
=
+
4
−
3
.
Now we can factor the left into two perfect squares,
(
x
−
2
)
2
=
1
.
Finally, we subtract
1
from both sides giving
(
x
−
2
)
2
−
1
. Our vertex is
h
,
k
giving
2
,
−
1
