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Mathematics
Mathematics
Problem
Consider the quadratic function
f
(
x
)
=
x
2
−
4
x
+
7
f(x)=x^{2}-4x+7
f
(
x
)
=
x
2
−
4
x
+
7
defined on the interval
[
−
1
,
5
]
[-1,5]
[
−
1
,
5
]
. a. (i) Rewrite
f
(
x
)
f(x)
f
(
x
)
in its vertex form. b. (ii) Find the minimum and maximum values of
f
(
x
)
f(x)
f
(
x
)
on
[
−
1
,
5
]
[-1,5]
[
−
1
,
5
]
. c. (iii) Hence determine the range of
f
f
f
on the interval
[
−
1
,
5
]
[-1,5]
[
−
1
,
5
]
.
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