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Math Problems
Algebra 2
Solve exponential equations by rewriting the base
For the following quadratic equation, find the discriminant.
\newline
x
2
+
4
x
+
32
=
2
x
x^{2}+4 x+32=2 x
x
2
+
4
x
+
32
=
2
x
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
−
x
2
+
4
x
+
11
=
8
x
−
1
-x^{2}+4 x+11=8 x-1
−
x
2
+
4
x
+
11
=
8
x
−
1
\newline
Answer:
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For the following quadratic equation, find the discriminant.
\newline
−
2
x
2
−
12
x
+
12
=
−
2
-2 x^{2}-12 x+12=-2
−
2
x
2
−
12
x
+
12
=
−
2
\newline
Answer:
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2
2
2
)
17
=
3
x
17=3^{x}
17
=
3
x
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Determine the value of
y
y
y
, if
x
x
x
is
−
5
-5
−
5
.
\newline
y
=
x
2
+
1
y=x^{2}+1
y
=
x
2
+
1
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
7
7
7
.
\newline
y
=
x
2
+
1
y=x^{2}+1
y
=
x
2
+
1
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
11
-11
−
11
.
\newline
y
=
x
2
+
1
y=x^{2}+1
y
=
x
2
+
1
\newline
Answer:
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Determine the value of
y
y
y
, if
x
x
x
is
−
2
-2
−
2
.
\newline
y
=
x
2
+
1
y=x^{2}+1
y
=
x
2
+
1
\newline
Answer:
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Solve the following equations:
\newline
1
1
1
)
8
t
=
6
8^{t}=6
8
t
=
6
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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an
(
x
,
y
)
(x, y)
(
x
,
y
)
point.
\newline
y
=
−
x
2
−
6
y=-x^{2}-6
y
=
−
x
2
−
6
\newline
Answer:
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Find the coordinates of the vertex of the following parabola algebraically. Write your answer as an
(
x
,
y
)
(x, y)
(
x
,
y
)
point.
\newline
y
=
−
x
2
+
10
x
−
26
y=-x^{2}+10 x-26
y
=
−
x
2
+
10
x
−
26
\newline
Answer:
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Find the coordinates of the vertex of the following parabola using graphing technology. Write your answer as an
(
x
,
y
)
(x, y)
(
x
,
y
)
point.
\newline
y
=
x
2
−
6
y=x^{2}-6
y
=
x
2
−
6
\newline
Answer:
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Find the equation of the axis of symmetry of the following parabola using graphing technology.
\newline
y
=
x
2
+
8
y=x^{2}+8
y
=
x
2
+
8
\newline
Answer:
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Find the value of
x
x
x
in the equation below.
\newline
18
=
x
+
5
18=x+5
18
=
x
+
5
\newline
Answer:
x
=
x=
x
=
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What is the value of
A
A
A
when we rewrite
2
x
−
6
+
2
x
2^{x-6}+2^{x}
2
x
−
6
+
2
x
as
A
⋅
2
x
A \cdot 2^{x}
A
⋅
2
x
?
\newline
A
=
A=
A
=
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Solve the exponential equation for
x
x
x
.
\newline
5
6
3
x
−
8
=
1
56^{3 x-8}=1
5
6
3
x
−
8
=
1
\newline
x
=
x=
x
=
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Solve the exponential equation for
x
x
x
.
\newline
2
6
9
x
+
5
=
1
26^{9 x+5}=1
2
6
9
x
+
5
=
1
\newline
x
=
x=
x
=
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Find the zeros of the function. Enter the solutions from least to greatest.
\newline
f
(
x
)
=
(
x
+
2
)
2
−
64
f(x)=(x+2)^{2}-64
f
(
x
)
=
(
x
+
2
)
2
−
64
\newline
lesser
x
=
x=
x
=
\newline
greater
x
=
x=
x
=
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Solve. Write your answer as an integer or a fraction in simplest form.
\newline
4
=
8
x
4 = 8^x
4
=
8
x
\newline
x
=
x=
x
=
______
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Solve for
x
x
x
.
\newline
5
x
=
1
5^x=1
5
x
=
1
\newline
\newline
Write your answer in simplest form.
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