Answer:
Set the polynomial equal to
y
to find the properties of the parabola.
y
=
x
2
+
16
x
+
8
Rewrite the equation in vertex form.
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y
=
(
x
+
8
)
2
−
56
Use the vertex form,
y
=
a
(
x
−
h
)
2
+
k
, to determine the values of
a
,
h
, and
k
.
a
=
1
h
=
−
8
k
=
−
56
Since the value of
a
is positive, the parabola opens up.
Opens Up
Find the vertex
(
h
,
k
)
.
(
−
8
,
−
56
)
Find
p
, the distance from the vertex to the focus.
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1
4
Find the focus.
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(
−
8
,
−
223
4
)
Find the axis of symmetry by finding the line that passes through the vertex and the focus.
x
=
−
8
Explanation: