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Math Problems
Algebra 2
Quadratic equation with complex roots
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
=
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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
=
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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
=
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Re-write the quadratic function below in Standard Form
\newline
y
=
−
4
(
x
+
2
)
2
−
4
y=-4(x+2)^{2}-4
y
=
−
4
(
x
+
2
)
2
−
4
\newline
Answer:
y
=
y=
y
=
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Re-write the quadratic function below in Standard Form
\newline
y
=
−
6
(
x
−
1
)
2
−
6
y=-6(x-1)^{2}-6
y
=
−
6
(
x
−
1
)
2
−
6
\newline
Answer:
y
=
y=
y
=
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Re-write the quadratic function below in Standard Form
\newline
y
=
−
8
(
x
+
1
)
2
+
9
y=-8(x+1)^{2}+9
y
=
−
8
(
x
+
1
)
2
+
9
\newline
Answer:
y
=
y=
y
=
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Re-write the quadratic function below in Standard Form
\newline
y
=
−
(
x
−
5
)
2
+
6
y=-(x-5)^{2}+6
y
=
−
(
x
−
5
)
2
+
6
\newline
Answer:
y
=
y=
y
=
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Re-write the quadratic function below in Standard Form
\newline
y
=
−
9
(
x
−
3
)
2
+
3
y=-9(x-3)^{2}+3
y
=
−
9
(
x
−
3
)
2
+
3
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
3
(
x
+
5
)
2
−
1
y=3(x+5)^{2}-1
y
=
3
(
x
+
5
)
2
−
1
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
4
(
x
−
1
)
2
+
4
y=4(x-1)^{2}+4
y
=
4
(
x
−
1
)
2
+
4
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
−
9
(
x
+
3
)
2
−
4
y=-9(x+3)^{2}-4
y
=
−
9
(
x
+
3
)
2
−
4
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
8
(
x
−
3
)
2
+
1
y=8(x-3)^{2}+1
y
=
8
(
x
−
3
)
2
+
1
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
7
(
x
−
2
)
2
+
2
y=7(x-2)^{2}+2
y
=
7
(
x
−
2
)
2
+
2
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
−
2
(
x
+
4
)
2
+
4
y=-2(x+4)^{2}+4
y
=
−
2
(
x
+
4
)
2
+
4
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
4
(
x
−
4
)
2
−
7
y=4(x-4)^{2}-7
y
=
4
(
x
−
4
)
2
−
7
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
3
(
x
+
1
)
2
−
4
y=3(x+1)^{2}-4
y
=
3
(
x
+
1
)
2
−
4
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
−
2
(
x
−
5
)
2
+
6
y=-2(x-5)^{2}+6
y
=
−
2
(
x
−
5
)
2
+
6
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
−
5
(
x
−
2
)
2
+
3
y=-5(x-2)^{2}+3
y
=
−
5
(
x
−
2
)
2
+
3
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
−
(
x
+
2
)
2
+
1
y=-(x+2)^{2}+1
y
=
−
(
x
+
2
)
2
+
1
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
−
3
(
x
−
2
)
2
−
8
y=-3(x-2)^{2}-8
y
=
−
3
(
x
−
2
)
2
−
8
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
−
7
(
x
+
1
)
2
+
6
y=-7(x+1)^{2}+6
y
=
−
7
(
x
+
1
)
2
+
6
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
−
5
(
x
+
3
)
2
−
8
y=-5(x+3)^{2}-8
y
=
−
5
(
x
+
3
)
2
−
8
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
−
7
(
x
−
3
)
2
+
4
y=-7(x-3)^{2}+4
y
=
−
7
(
x
−
3
)
2
+
4
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
7
(
x
+
2
)
2
+
8
y=7(x+2)^{2}+8
y
=
7
(
x
+
2
)
2
+
8
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
9
(
x
+
1
)
2
+
6
y=9(x+1)^{2}+6
y
=
9
(
x
+
1
)
2
+
6
\newline
Answer:
y
=
y=
y
=
Get tutor help
Re-write the quadratic function below in Standard Form
\newline
y
=
4
(
x
+
3
)
2
+
6
y=4(x+3)^{2}+6
y
=
4
(
x
+
3
)
2
+
6
\newline
Answer:
y
=
y=
y
=
Get tutor help
Use the quadratic formula to solve. Express your answer in simplest form.
\newline
16
p
2
+
2
p
−
15
=
−
6
p
16 p^{2}+2 p-15=-6 p
16
p
2
+
2
p
−
15
=
−
6
p
\newline
Answer:
p
=
p=
p
=
Get tutor help
Use the quadratic formula to solve. Express your answer in simplest form.
\newline
15
q
2
−
14
q
−
8
=
0
15 q^{2}-14 q-8=0
15
q
2
−
14
q
−
8
=
0
\newline
Answer:
q
=
q=
q
=
Get tutor help
x
2
y
(
2
x
y
2
−
7
x
y
+
5
x
−
4
y
)
x^{2} y\left(2 x y^{2}-7 x y+5 x-4 y\right)
x
2
y
(
2
x
y
2
−
7
x
y
+
5
x
−
4
y
)
Get tutor help
Solve the quadratic equation:
(
2
x
2
−
5
x
+
3
=
0
)
(2x^2-5x+3=0)
(
2
x
2
−
5
x
+
3
=
0
)
Get tutor help
A curve is defined by the parametric equations
x
(
t
)
=
−
10
t
2
+
6
t
x(t)=-10 t^{2}+6 t
x
(
t
)
=
−
10
t
2
+
6
t
and
y
(
t
)
=
−
4
t
3
−
8
t
2
y(t)=-4 t^{3}-8 t^{2}
y
(
t
)
=
−
4
t
3
−
8
t
2
. Find
d
y
d
x
\frac{d y}{d x}
d
x
d
y
.
\newline
Answer:
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Compute the derivatives
\newline
f
(
x
)
=
ln
(
2
x
x
+
1
)
3
f(x)=\ln \left(\frac{2x}{x+1}\right)^3
f
(
x
)
=
ln
(
x
+
1
2
x
)
3
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\newline
Discuss the nature of the roots of the quadratic equation
\newline
(
a
2
+
b
2
)
x
2
−
3
(
a
−
b
)
x
+
9
2
=
0
,
a
+
b
≠
0
(a^{2}+b^{2})x^{2}-3(a-b)x+\frac{9}{2}=0,\quad a+b\neq 0
(
a
2
+
b
2
)
x
2
−
3
(
a
−
b
)
x
+
2
9
=
0
,
a
+
b
=
0
Get tutor help
y
=
−
(
x
−
5
)
2
+
9
y=-(x-5)^{2}+9
y
=
−
(
x
−
5
)
2
+
9
\newline
The given equation represents a parabola in the
x
y
x y
x
y
-plane. Which of the following equivalent forms of the equation displays the
x
x
x
-intercepts of the parabola as constants or coefficients?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
−
x
2
+
10
x
−
16
y=-x^{2}+10 x-16
y
=
−
x
2
+
10
x
−
16
\newline
(B)
y
=
−
(
x
−
8
)
(
x
−
2
)
y=-(x-8)(x-2)
y
=
−
(
x
−
8
)
(
x
−
2
)
\newline
(C)
y
=
−
(
x
−
7
)
(
x
−
3
)
+
5
y=-(x-7)(x-3)+5
y
=
−
(
x
−
7
)
(
x
−
3
)
+
5
\newline
(D)
y
=
−
x
(
x
−
10
)
−
16
y=-x(x-10)-16
y
=
−
x
(
x
−
10
)
−
16
Get tutor help
Which of the following is equivalent to the complex number
\newline
i
32
i^{32}
i
32
?
\newline
Choose
1
1
1
answer:
\newline
(A)
1
1
1
\newline
(B)
i
i
i
\newline
(C)
−
1
-1
−
1
\newline
(D)
−
i
-i
−
i
Get tutor help
Find the Roots of the quadratic equation
\newline
x
2
−
3
x
−
10
=
0
x^{2}-3x-10=0
x
2
−
3
x
−
10
=
0
using Factorization method
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d
y
d
x
=
3
y
\frac{d y}{d x}=3 y
d
x
d
y
=
3
y
, and
y
=
2
y=2
y
=
2
when
x
=
1
x=1
x
=
1
.
\newline
Solve the equation.
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
e
3
x
−
6
y=e^{3 x-6}
y
=
e
3
x
−
6
\newline
(B)
y
=
2
e
3
x
+
1
y=2 e^{3 x+1}
y
=
2
e
3
x
+
1
\newline
(C)
y
=
2
e
3
x
+
3
y=2 e^{3 x+3}
y
=
2
e
3
x
+
3
\newline
(D)
y
=
2
e
3
x
−
3
y=2 e^{3 x-3}
y
=
2
e
3
x
−
3
Get tutor help
d
y
d
x
=
3
y
\frac{d y}{d x}=3 y
d
x
d
y
=
3
y
, and
y
=
2
y=2
y
=
2
when
x
=
1
x=1
x
=
1
.
\newline
Solve the equation.
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
e
3
x
−
6
y=e^{3 x-6}
y
=
e
3
x
−
6
\newline
(B)
y
=
2
e
3
x
−
3
y=2 e^{3 x-3}
y
=
2
e
3
x
−
3
\newline
(C)
y
=
2
e
3
x
+
3
y=2 e^{3 x+3}
y
=
2
e
3
x
+
3
\newline
(D)
y
=
2
e
3
x
+
1
y=2 e^{3 x+1}
y
=
2
e
3
x
+
1
Get tutor help
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