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Math Problems
Algebra 2
Quadratic equation with complex roots
Which equations define
y
y
y
as a linear function of
x
x
x
? Select all that apply.
\newline
Multi-select Choices:
\newline
(A)
y
=
5
x
3
y = 5x^3
y
=
5
x
3
\newline
(B)
y
−
4
=
x
5
y - 4 = x^5
y
−
4
=
x
5
\newline
(C)
−
3
y
=
12
-3y = 12
−
3
y
=
12
\newline
(D)
y
=
4
x
2
5
y = \frac{4x^2}{5}
y
=
5
4
x
2
\newline
(E)
y
=
−
2
+
12
x
y = -2 + 12x
y
=
−
2
+
12
x
\newline
(F)
3
x
−
y
=
9
3x - y = 9
3
x
−
y
=
9
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Which equations define
y
y
y
as a linear function of
x
x
x
? Select all that apply.
\newline
Multi-select Choices:
\newline
(A)
y
=
27
3
y = \sqrt[3]{27}
y
=
3
27
\newline
(B)
y
=
5
x
+
9
y = 5x + 9
y
=
5
x
+
9
\newline
(C)
4
y
=
4
x
2
−
8
4y = 4x^2 - 8
4
y
=
4
x
2
−
8
\newline
(D)
y
=
2
5
+
x
y = \frac{2}{5} + x
y
=
5
2
+
x
\newline
(E)
x
−
y
=
10
x - y = 10
x
−
y
=
10
\newline
(F)
y
=
8
x
−
2
x
+
4
y = 8x - 2x + 4
y
=
8
x
−
2
x
+
4
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Select all of the equations below that are equivalent to:
\newline
p
+
q
=
33
p + q = 33
p
+
q
=
33
\newline
Use properties of equality.
\newline
Multi-select Choices:
\newline
(A)
(
p
+
q
)
⋅
−
3
=
−
99
(p + q) \cdot -3 = -99
(
p
+
q
)
⋅
−
3
=
−
99
\newline
(B)
(
p
+
q
)
⋅
2
=
66
(p + q) \cdot 2 = 66
(
p
+
q
)
⋅
2
=
66
\newline
(C)
3
(
p
+
q
)
=
99
3(p + q) = 99
3
(
p
+
q
)
=
99
\newline
(D)
(
p
+
q
)
⋅
−
2
=
−
66
(p + q) \cdot -2 = -66
(
p
+
q
)
⋅
−
2
=
−
66
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Solve the quadratic equation
x
2
−
x
−
6
=
0
x^{2}-x-6=0
x
2
−
x
−
6
=
0
by factoring
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f
(
x
)
=
x
2
−
6
x
−
7
f(x)=x^{2}-6x-7
f
(
x
)
=
x
2
−
6
x
−
7
\newline
Which of the following is an equivalent form of the function
f
f
f
in which the zeros of
f
f
f
appear as constants or coefficients?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
(
x
)
=
(
x
−
7
)
(
x
+
1
)
f(x)=(x-7)(x+1)
f
(
x
)
=
(
x
−
7
)
(
x
+
1
)
\newline
(B)
f
(
x
)
=
(
x
−
1
)
(
x
+
7
)
f(x)=(x-1)(x+7)
f
(
x
)
=
(
x
−
1
)
(
x
+
7
)
\newline
(C)
f
(
x
)
=
x
(
x
−
6
)
−
7
f(x)=x(x-6)-7
f
(
x
)
=
x
(
x
−
6
)
−
7
\newline
(D)
f
(
x
)
=
(
x
−
6
)
2
−
7
f(x)=(x-6)^{2}-7
f
(
x
)
=
(
x
−
6
)
2
−
7
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Use the Quadratic Formula to solve the quadratic below:
\newline
x
2
−
5
x
+
9
=
0
x^{2}-5x+9=0
x
2
−
5
x
+
9
=
0
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Use the Quadratic Formula to solve the quadratic below
\newline
x
2
−
5
x
+
9
=
0
x^{2}-5 x+9=0
x
2
−
5
x
+
9
=
0
\newline
Desmos Scientific Calculator
\newline
Show Your Work
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Solve using the quadra
\newline
a)
x
2
=
2
x
+
1
x^{2}=2 x+1
x
2
=
2
x
+
1
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Which equation represents a linear function?
\newline
(A)
y
=
−
x
2
−
4
y=-x^{2}-4
y
=
−
x
2
−
4
\newline
(B)
−
3
x
2
+
1
=
y
-3 x^{2}+1=y
−
3
x
2
+
1
=
y
\newline
(C)
y
=
x
2
y=x^{2}
y
=
x
2
\newline
(D)
x
+
2
=
y
x+2=y
x
+
2
=
y
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y
=
x
2
+
x
+
1
3
y=\sqrt[3]{x^{2}+x+1}
y
=
3
x
2
+
x
+
1
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Find the equation of the tangent line to
\newline
x
=
t
3
x=\sqrt[3]{t}
x
=
3
t
and
y
=
1
2
(
t
2
−
2
)
y=\frac{1}{2}(t^{2}-2)
y
=
2
1
(
t
2
−
2
)
at the point
(
2
,
31
)
(2,31)
(
2
,
31
)
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Which equation shows the commutative property of multiplication?
\newline
Choices:
\newline
(A)
f
⋅
(
g
⋅
h
)
=
(
f
⋅
g
)
⋅
h
f \cdot (g \cdot h) = (f \cdot g) \cdot h
f
⋅
(
g
⋅
h
)
=
(
f
⋅
g
)
⋅
h
\newline
(B)
f
⋅
0
=
0
f \cdot 0 = 0
f
⋅
0
=
0
\newline
(C)
f
⋅
g
=
g
⋅
f
f \cdot g = g \cdot f
f
⋅
g
=
g
⋅
f
\newline
(D)
h
=
f
⋅
g
h = f \cdot g
h
=
f
⋅
g
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(
t
+
1
)
2
+
c
=
0
(t+1)^{2}+c=0
(
t
+
1
)
2
+
c
=
0
\newline
In the given equation,
c
c
c
is a constant. The equation has solutions at
t
=
3
2
t=\frac{3}{2}
t
=
2
3
and
t
=
−
7
2
t=-\frac{7}{2}
t
=
−
2
7
. What is the value of
c
c
c
?
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(
a
x
+
5
)
(
x
+
v
)
=
a
x
2
+
25
x
+
25
(a x+5)(x+v)=a x^{2}+25 x+25
(
a
x
+
5
)
(
x
+
v
)
=
a
x
2
+
25
x
+
25
\newline
What is the value of
a
a
a
in the given equation?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
5
-5
−
5
\newline
(B)
−
4
-4
−
4
\newline
(C)
4
4
4
\newline
(D)
5
5
5
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Select all of the equations below that are equivalent to:
\newline
9
=
n
+
−
3
9 = n + -3
9
=
n
+
−
3
\newline
Use properties of equality.
\newline
Multi-select Choices:
\newline
(A)
64
=
(
n
+
(
−
3
)
)
⋅
8
64 = (n + (-3)) \cdot 8
64
=
(
n
+
(
−
3
))
⋅
8
\newline
(B)
−
77
=
−
7
(
n
+
(
−
3
)
)
-77 = -7(n + (-3))
−
77
=
−
7
(
n
+
(
−
3
))
\newline
(C)
90
=
(
n
+
(
−
3
)
)
⋅
10
90 = (n + (-3)) \cdot 10
90
=
(
n
+
(
−
3
))
⋅
10
\newline
(D)
63
=
(
n
+
(
−
3
)
)
⋅
7
63 = (n + (-3)) \cdot 7
63
=
(
n
+
(
−
3
))
⋅
7
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Re-write the quadratic function below in Standard Form:
y
=
−
6
(
x
−
1
)
(
x
−
5
)
y= -6(x-1)(x-5)
y
=
−
6
(
x
−
1
)
(
x
−
5
)
Get tutor help
Evaluate
lim
x
→
10
x
2
−
100
x
−
9
\lim_{x \to 10}\frac{x^{2}-100}{x-9}
lim
x
→
10
x
−
9
x
2
−
100
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Use the quadratic formula to solve. Express your answer in simplest form.
\newline
3
c
2
+
14
c
−
8
=
4
c
3c^{2}+14c-8=4c
3
c
2
+
14
c
−
8
=
4
c
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A quadratic equation is in the form
a
x
2
+
b
x
+
c
=
0
ax^2+bx+c=0
a
x
2
+
b
x
+
c
=
0
. If the roots of the quadratic equation
2
x
2
−
4
x
+
k
=
0
2x^2-4x+k=0
2
x
2
−
4
x
+
k
=
0
are real and equal, find the value of
k
k
k
.
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Find the zeros of the following quadratic function using the square root method. What are the
x
x
x
-intercepts of the graph of the function?
\newline
F
(
x
)
=
(
2
x
+
9
)
2
−
32
F(x)=(2 x+9)^{2}-32
F
(
x
)
=
(
2
x
+
9
)
2
−
32
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Find the zeros of the quadratic function using the square root method. What are the
x
x
x
-intercepts of the graph of the function?
\newline
g
(
x
)
=
(
x
−
3
)
2
−
1
g(x)=(x-3)^{2}-1
g
(
x
)
=
(
x
−
3
)
2
−
1
Get tutor help
Find the zeros of the following quadratic function using the square root method. What are the x-intercepts of the graph of the function?
\newline
f
(
x
)
=
x
2
−
50
f(x)=x^{2}-50
f
(
x
)
=
x
2
−
50
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Write the quadratic equation in standard form:
\newline
3
x
2
−
x
−
16
=
4
3 x^{2}-x-16=4
3
x
2
−
x
−
16
=
4
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
−
x
2
−
x
=
11
-x^{2}-x=11
−
x
2
−
x
=
11
\newline
Answer:
Get tutor help
Write the quadratic equation in standard form:
\newline
−
4
x
2
+
x
+
24
=
4
-4 x^{2}+x+24=4
−
4
x
2
+
x
+
24
=
4
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
x
+
3
=
−
3
x
2
x+3=-3 x^{2}
x
+
3
=
−
3
x
2
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
8
x
−
19
=
5
x
2
8 x-19=5 x^{2}
8
x
−
19
=
5
x
2
\newline
Answer:
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Solve the equation by factoring:
\newline
8
x
+
6
x
2
−
2
x
3
=
0
8 x+6 x^{2}-2 x^{3}=0
8
x
+
6
x
2
−
2
x
3
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve the equation by factoring:
\newline
x
3
−
11
x
2
+
10
x
=
0
x^{3}-11 x^{2}+10 x=0
x
3
−
11
x
2
+
10
x
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Write the quadratic equation in standard form:
\newline
5
x
2
−
5
x
−
14
=
x
5 x^{2}-5 x-14=x
5
x
2
−
5
x
−
14
=
x
\newline
Answer:
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Solve the equation by factoring:
\newline
x
3
−
8
x
2
−
9
x
=
0
x^{3}-8 x^{2}-9 x=0
x
3
−
8
x
2
−
9
x
=
0
\newline
Answer:
x
=
x=
x
=
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Write the quadratic equation in standard form:
\newline
x
2
+
1
=
8
x
x^{2}+1=8 x
x
2
+
1
=
8
x
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
6
x
−
9
=
−
5
x
2
6 x-9=-5 x^{2}
6
x
−
9
=
−
5
x
2
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
−
x
2
−
8
x
−
15
=
4
x
2
-x^{2}-8 x-15=4 x^{2}
−
x
2
−
8
x
−
15
=
4
x
2
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
7
x
+
3
=
3
x
2
7 x+3=3 x^{2}
7
x
+
3
=
3
x
2
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
−
x
2
+
x
+
10
=
−
3
x
2
-x^{2}+x+10=-3 x^{2}
−
x
2
+
x
+
10
=
−
3
x
2
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
−
4
x
+
19
=
4
x
2
-4 x+19=4 x^{2}
−
4
x
+
19
=
4
x
2
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
x
2
−
3
x
+
5
=
−
4
x
2
x^{2}-3 x+5=-4 x^{2}
x
2
−
3
x
+
5
=
−
4
x
2
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
2
x
2
−
3
x
−
13
=
−
2
2 x^{2}-3 x-13=-2
2
x
2
−
3
x
−
13
=
−
2
\newline
Answer:
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Solve the equation by factoring:
\newline
x
3
−
9
x
2
+
18
x
=
0
x^{3}-9 x^{2}+18 x=0
x
3
−
9
x
2
+
18
x
=
0
\newline
Answer:
x
=
x=
x
=
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Solve the equation by factoring:
\newline
x
3
−
2
x
2
−
48
x
=
0
x^{3}-2 x^{2}-48 x=0
x
3
−
2
x
2
−
48
x
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve the equation by factoring:
\newline
8
x
+
7
x
2
−
x
3
=
0
8 x+7 x^{2}-x^{3}=0
8
x
+
7
x
2
−
x
3
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Solve the equation by factoring:
\newline
3
x
3
−
9
x
2
−
12
x
=
0
3 x^{3}-9 x^{2}-12 x=0
3
x
3
−
9
x
2
−
12
x
=
0
\newline
Answer:
x
=
x=
x
=
Get tutor help
Write the quadratic equation in standard form:
\newline
4
x
2
+
6
x
−
5
=
5
4 x^{2}+6 x-5=5
4
x
2
+
6
x
−
5
=
5
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
−
3
x
2
−
9
x
+
4
=
−
3
x
-3 x^{2}-9 x+4=-3 x
−
3
x
2
−
9
x
+
4
=
−
3
x
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
−
x
2
−
6
=
−
6
x
-x^{2}-6=-6 x
−
x
2
−
6
=
−
6
x
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
5
x
2
+
4
x
−
16
=
−
4
5 x^{2}+4 x-16=-4
5
x
2
+
4
x
−
16
=
−
4
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
3
x
2
−
5
x
=
−
5
3 x^{2}-5 x=-5
3
x
2
−
5
x
=
−
5
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
4
x
+
3
=
x
2
4 x+3=x^{2}
4
x
+
3
=
x
2
\newline
Answer:
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Write the quadratic equation in standard form:
\newline
6
x
2
+
7
x
−
9
=
4
x
2
6 x^{2}+7 x-9=4 x^{2}
6
x
2
+
7
x
−
9
=
4
x
2
\newline
Answer:
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