Explanation:
Firstly, complete the square to put the equation in vertex form,
y
=
−
(
x
+
3
)
2
+
1
This implies that the vertex, or local maximum (since this is a negative quadratic) is
(
−
3
,
1
)
. This can be plotted.
The quadratic can also be factorised,
y
=
−
(
x
+
2
)
(
x
+
4
)
which tells us that the quadratic has roots of -2 and -4, and crosses the
x
a
ξ
s
at these points.
Finally, we observe that if we plug
x
=
0
into the original equation,
y
=
−
8
, so this is the
y
intercept.
All of this gives us enough information to sketch the curve:
graph{-x^2-6x-8 [-10, 10, -5, 5]}