plot some quadratic expressions in a graph.
(Any quadratic expressions - your choice)
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1
Answer:
Step-by-step explanation:
Plot the graph of
Q
(
x
)
:
2
x
2
+
5
x
+
2
.
Solution: Step-1:
a
=
2
>
0
, so the parabola will open upward.
Step-2:
2
x
2
+
5
x
+
2
=
(
2
x
+
1
)
(
x
+
2
)
, so the zeroes of the expression are
x
=
−
1
2
,
x
=
−
2
. These are the points where the parabola will cross the horizontal axis.
Step-3: The discriminant is
D
=
9
(verify). The coordinates of the vertex are
V
≡
(
−
b
2
a
,
−
D
4
a
)
or
V
≡
(
−
5
4
,
−
9
8
)
. This will be the lowermost point on the parabola.
Step-4: We calculate
Q
(
x
)
for some specific values of x. For example,
Q
(
0
)
=
2
,
Q
(
−
3
)
=
5
, etc.
Using all this information, the graph can now be plotted easily:
Parabola plotted graph
Attachments:
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