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Let’s check out your problem:
let
h
(
x
)
=
x
2
+
k
x
−
4
h(x)=x^2+kx-4
h
(
x
)
=
x
2
+
k
x
−
4
. If
h
(
−
3
)
=
−
7
h(-3)=-7
h
(
−
3
)
=
−
7
, what is the value of
h
(
2
)
h(2)
h
(
2
)
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Math Problems
Precalculus
Complex conjugate theorem
Full solution
Q.
let
h
(
x
)
=
x
2
+
k
x
−
4
h(x)=x^2+kx-4
h
(
x
)
=
x
2
+
k
x
−
4
. If
h
(
−
3
)
=
−
7
h(-3)=-7
h
(
−
3
)
=
−
7
, what is the value of
h
(
2
)
h(2)
h
(
2
)
Calculate
k
k
k
:
Calculate
h
(
−
3
)
h(-3)
h
(
−
3
)
to find
k
k
k
:
h
(
−
3
)
=
(
−
3
)
2
+
k
(
−
3
)
−
4
=
9
−
3
k
−
4
=
5
−
3
k
.
h(-3) = (-3)^2 + k(-3) - 4 = 9 - 3k - 4 = 5 - 3k.
h
(
−
3
)
=
(
−
3
)
2
+
k
(
−
3
)
−
4
=
9
−
3
k
−
4
=
5
−
3
k
.
Set
h
(
−
3
)
=
−
7
h(-3) = -7
h
(
−
3
)
=
−
7
:
5
−
3
k
=
−
7.
5 - 3k = -7.
5
−
3
k
=
−
7.
Solve for
k
k
k
:
−
3
k
=
−
7
−
5
-3k = -7 - 5
−
3
k
=
−
7
−
5
,
−
3
k
=
−
12
-3k = -12
−
3
k
=
−
12
,
k
=
4.
k = 4.
k
=
4.
Substitute
k
k
k
into
h
(
x
)
h(x)
h
(
x
)
:
Substitute
k
=
4
k = 4
k
=
4
into
h
(
x
)
h(x)
h
(
x
)
and calculate
h
(
2
)
h(2)
h
(
2
)
:
\newline
h
(
x
)
=
x
2
+
4
x
−
4.
h(x) = x^2 + 4x - 4.
h
(
x
)
=
x
2
+
4
x
−
4.
\newline
h
(
2
)
=
(
2
)
2
+
4
(
2
)
−
4
=
4
+
8
−
4
=
8.
h(2) = (2)^2 + 4(2) - 4 = 4 + 8 - 4 = 8.
h
(
2
)
=
(
2
)
2
+
4
(
2
)
−
4
=
4
+
8
−
4
=
8.
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−
9
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)
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4
r
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)
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\newline
(
x
+
7
)
(
x
+
4
)
(x + 7)(x + 4)
(
x
+
7
)
(
x
+
4
)
\newline
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\newline
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=
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