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Byju's Answer
Standard XII
Mathematics
Range of a Quadratic Expression
The range of ...
Question
The range of
f
(
x
)
=
−
x
2
+
7
x
+
60
in
x
∈
[
−
3
,
2
]
is
A
[
70
,
289
4
]
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B
[
30
,
289
4
]
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C
[
30
,
70
]
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D
[
30
,
289
4
)
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Solution
The correct option is
C
[
30
,
70
]
f
(
x
)
=
−
x
2
+
7
x
+
60
For given function
a
<
0
,
b
>
0
and
c
=
60
∴
vertex of
y
=
f
(
x
)
will be in
1
st
quadrant, so the graph will be
x
coordinate of the vertex is
−
b
2
a
=
7
2
∉
[
−
3
,
2
]
∵
Vertex is in right of the given interval.
∴
Range for given condition is
[
f
(
−
3
)
,
f
(
2
)
]
≡
[
30
,
70
]
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