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Math Problems
Algebra 2
Composition of linear and quadratic functions: find an equation
Given the function
f
(
x
)
=
5
x
2
−
1
f(x)=5 x^{2}-1
f
(
x
)
=
5
x
2
−
1
, then what is
f
(
x
)
+
3
f(x)+3
f
(
x
)
+
3
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
1
+
5
x
2
f(x)=-1+5 x^{2}
f
(
x
)
=
−
1
+
5
x
2
, then what is
f
(
x
)
−
3
f(x)-3
f
(
x
)
−
3
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
6
−
x
2
f(x)=-6-x^{2}
f
(
x
)
=
−
6
−
x
2
, then what is
−
f
(
x
)
-f(x)
−
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
2
−
6
x
2
f(x)=2-6 x^{2}
f
(
x
)
=
2
−
6
x
2
, then what is
−
f
(
x
)
-f(x)
−
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
3
+
6
x
2
f(x)=3+6 x^{2}
f
(
x
)
=
3
+
6
x
2
, then what is
f
(
−
x
)
f(-x)
f
(
−
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
6
−
x
2
f(x)=-6-x^{2}
f
(
x
)
=
−
6
−
x
2
, then what is
f
(
x
)
−
2
f(x)-2
f
(
x
)
−
2
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
1
+
3
x
2
f(x)=-1+3 x^{2}
f
(
x
)
=
−
1
+
3
x
2
, then what is
f
(
x
)
+
3
f(x)+3
f
(
x
)
+
3
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
4
x
2
−
3
f(x)=-4 x^{2}-3
f
(
x
)
=
−
4
x
2
−
3
, then what is
f
(
x
−
1
)
f(x-1)
f
(
x
−
1
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
4
x
2
+
5
f(x)=-4 x^{2}+5
f
(
x
)
=
−
4
x
2
+
5
, then what is
f
(
x
−
2
)
f(x-2)
f
(
x
−
2
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
2
+
5
x
2
f(x)=-2+5 x^{2}
f
(
x
)
=
−
2
+
5
x
2
, then what is
f
(
x
)
−
1
f(x)-1
f
(
x
)
−
1
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
2
x
2
−
x
f(x)=-2 x^{2}-x
f
(
x
)
=
−
2
x
2
−
x
, then what is
f
(
x
)
+
2
f(x)+2
f
(
x
)
+
2
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
x
+
6
x
3
f(x)=-x+6 x^{3}
f
(
x
)
=
−
x
+
6
x
3
, then what is
f
(
x
)
−
2
f(x)-2
f
(
x
)
−
2
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
6
x
2
−
1
f(x)=6 x^{2}-1
f
(
x
)
=
6
x
2
−
1
, then what is
−
2
f
(
x
)
-2 f(x)
−
2
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
5
x
2
+
1
f(x)=5 x^{2}+1
f
(
x
)
=
5
x
2
+
1
, then what is
2
f
(
x
)
2 f(x)
2
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
5
2
x
3
+
1
6
x
2
f(x)=\frac{5}{2} x^{3}+\frac{1}{6} x^{2}
f
(
x
)
=
2
5
x
3
+
6
1
x
2
, then what is
−
2
f
(
x
)
-2 f(x)
−
2
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
1
6
x
−
x
2
f(x)=-\frac{1}{6} x-x^{2}
f
(
x
)
=
−
6
1
x
−
x
2
, then what is
f
(
−
3
x
)
f(-3 x)
f
(
−
3
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
6
5
+
3
2
x
2
f(x)=\frac{6}{5}+\frac{3}{2} x^{2}
f
(
x
)
=
5
6
+
2
3
x
2
, then what is
f
(
x
−
2
)
f(x-2)
f
(
x
−
2
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
x
−
1
6
x
2
f(x)=-x-\frac{1}{6} x^{2}
f
(
x
)
=
−
x
−
6
1
x
2
, then what is
f
(
−
3
x
)
f(-3 x)
f
(
−
3
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
1
4
x
+
3
2
x
3
f(x)=\frac{1}{4} x+\frac{3}{2} x^{3}
f
(
x
)
=
4
1
x
+
2
3
x
3
, then what is
−
f
(
x
)
-f(x)
−
f
(
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
x
2
+
1
2
x
f(x)=x^{2}+\frac{1}{2} x
f
(
x
)
=
x
2
+
2
1
x
, then what is
f
(
x
)
−
1
f(x)-1
f
(
x
)
−
1
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
5
3
x
2
−
3
5
x
f(x)=-\frac{5}{3} x^{2}-\frac{3}{5} x
f
(
x
)
=
−
3
5
x
2
−
5
3
x
, then what is
f
(
x
+
2
)
f(x+2)
f
(
x
+
2
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
x
2
+
1
2
f(x)=-x^{2}+\frac{1}{2}
f
(
x
)
=
−
x
2
+
2
1
, then what is
f
(
x
−
1
)
f(x-1)
f
(
x
−
1
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
1
3
x
2
−
1
2
x
f(x)=-\frac{1}{3} x^{2}-\frac{1}{2} x
f
(
x
)
=
−
3
1
x
2
−
2
1
x
, then what is
f
(
−
3
x
)
f(-3 x)
f
(
−
3
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
x
2
+
1
4
f(x)=-x^{2}+\frac{1}{4}
f
(
x
)
=
−
x
2
+
4
1
, then what is
f
(
x
+
2
)
f(x+2)
f
(
x
+
2
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
2
x
−
1
4
x
2
f(x)=-2 x-\frac{1}{4} x^{2}
f
(
x
)
=
−
2
x
−
4
1
x
2
, then what is
f
(
x
−
2
)
f(x-2)
f
(
x
−
2
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
5
x
3
+
2
5
x
f(x)=5 x^{3}+\frac{2}{5} x
f
(
x
)
=
5
x
3
+
5
2
x
, then what is
f
(
x
)
+
2
f(x)+2
f
(
x
)
+
2
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
3
2
−
x
2
f(x)=-\frac{3}{2}-x^{2}
f
(
x
)
=
−
2
3
−
x
2
, then what is
f
(
x
+
2
)
f(x+2)
f
(
x
+
2
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
4
3
x
2
−
2
3
f(x)=-\frac{4}{3} x^{2}-\frac{2}{3}
f
(
x
)
=
−
3
4
x
2
−
3
2
, then what is
f
(
x
)
−
3
f(x)-3
f
(
x
)
−
3
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
1
6
−
4
x
2
f(x)=-\frac{1}{6}-4 x^{2}
f
(
x
)
=
−
6
1
−
4
x
2
, then what is
f
(
3
x
)
f(3 x)
f
(
3
x
)
as a simplified polynomial?
\newline
Answer:
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Given the function
f
(
x
)
=
−
x
−
4
5
x
2
f(x)=-x-\frac{4}{5} x^{2}
f
(
x
)
=
−
x
−
5
4
x
2
, then what is
f
(
x
−
3
)
f(x-3)
f
(
x
−
3
)
as a simplified polynomial?
\newline
Answer:
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37
37
37
.
y
=
x
a
x
⇒
a
x
−
1
=
y=x a^{x} \Rightarrow a^{x-1}=
y
=
x
a
x
⇒
a
x
−
1
=
?
\newline
A)
y
x
−
1
\frac{y}{x-1}
x
−
1
y
\newline
B)
1
x
(
a
−
1
)
\frac{1}{x(a-1)}
x
(
a
−
1
)
1
\newline
C)
y
−
1
x
−
1
\frac{y-1}{x-1}
x
−
1
y
−
1
\newline
D)
y
a
x
\frac{y}{a x}
a
x
y
\newline
E)
y
−
x
x
\frac{y-x}{x}
x
y
−
x
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It is given that
10
x
3
+
5
x
2
−
x
+
4
=
(
2
x
−
1
)
(
x
+
3
)
Q
(
x
)
+
A
x
+
B
10 x^{3}+5 x^{2}-x+4=(2 x-1)(x+3) \mathrm{Q}(x)+A x+B
10
x
3
+
5
x
2
−
x
+
4
=
(
2
x
−
1
)
(
x
+
3
)
Q
(
x
)
+
A
x
+
B
, where
Q
(
x
)
\mathrm{Q}(x)
Q
(
x
)
is a polynomial. Find the values of the constants
A
A
A
and
B
B
B
.
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For the function,
f
(
x
)
=
x
2
−
3
x
+
9
f(x)=x^{2}-3 x+9
f
(
x
)
=
x
2
−
3
x
+
9
\newline
Find when
f
(
x
)
=
7
f(x)=7
f
(
x
)
=
7
.
\newline
x
=
□
x= \square
x
=
□
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Question
\newline
Given the function
f
(
x
)
=
−
2
x
2
−
x
f(x)=-2 x^{2}-x
f
(
x
)
=
−
2
x
2
−
x
, express the value of
f
(
x
+
h
)
−
f
(
x
)
h
\frac{f(x+h)-f(x)}{h}
h
f
(
x
+
h
)
−
f
(
x
)
in simplest form.
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
Submit Answer
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Add.
\newline
Your answer should be an expanded polynomial in standard form.
\newline
(
−
2
k
3
−
7
k
2
+
5
k
)
+
(
6
k
2
+
3
k
)
=
\left(-2 k^{3}-7 k^{2}+5 k\right)+\left(6 k^{2}+3 k\right)=
(
−
2
k
3
−
7
k
2
+
5
k
)
+
(
6
k
2
+
3
k
)
=
Get tutor help
Google Classroom
\newline
If
(
x
,
y
)
(x, y)
(
x
,
y
)
is a solution to the system of equations shown, what is the product of the
y
y
y
-coordinates of the solutions?
\newline
x
2
+
y
2
=
9
x^{2}+y^{2}=9
x
2
+
y
2
=
9
\newline
x
+
y
=
3
x+y=3
x
+
y
=
3
Get tutor help
What is the value of the expression below when
y
=
4
y=4
y
=
4
?
\newline
y
2
+
7
y
+
9
y^{2}+7 y+9
y
2
+
7
y
+
9
\newline
Answer:
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What is the value of the expression below when
z
=
5
z=5
z
=
5
?
\newline
z
2
−
z
+
6
z^{2}-z+6
z
2
−
z
+
6
\newline
Answer:
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Divide the polynomials. Your answer should be a polynomial.
\newline
x
2
+
2
x
x
=
□
\frac{x^{2}+2 x}{x}=\square
x
x
2
+
2
x
=
□
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M
=
5
w
4
−
7
w
2
z
2
−
3
z
4
M=5 w^{4}-7 w^{2} z^{2}-3 z^{4}
M
=
5
w
4
−
7
w
2
z
2
−
3
z
4
\newline
N
=
−
w
4
+
13
w
2
z
2
−
4
z
4
M
+
N
=
□
\begin{array}{l} N=-w^{4}+13 w^{2} z^{2}-4 z^{4} \\ M+N=\square \end{array}
N
=
−
w
4
+
13
w
2
z
2
−
4
z
4
M
+
N
=
□
\newline
Your answer should be a polynomial in standa
Get tutor help
X
=
−
4
a
2
+
3
a
b
+
12
b
2
X=-4 a^{2}+3 a b+12 b^{2}
X
=
−
4
a
2
+
3
ab
+
12
b
2
\newline
Y
=
9
a
2
+
a
b
−
7
b
2
Y=9 a^{2}+a b-7 b^{2}
Y
=
9
a
2
+
ab
−
7
b
2
\newline
Y
+
X
=
Y+X=
Y
+
X
=
\newline
Your answer should be a polynomial in standard form.
Get tutor help
p
=
4
a
2
−
2
a
b
+
9
b
2
p=4a^2-2ab+9b^2
p
=
4
a
2
−
2
ab
+
9
b
2
q
=
7
a
2
−
3
a
b
+
5
b
2
q=7a^2-3ab+5b^2
q
=
7
a
2
−
3
ab
+
5
b
2
p
−
q
=
p-q=
p
−
q
=
your answer should be a polynomial in standard form
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Rewrite the following polynomial in standard form.
\newline
x
−
9
+
x
2
2
x-9+\frac{x^{2}}{2}
x
−
9
+
2
x
2
\newline
Answer Attempt
2
2
2
out of
2
2
2
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Question
\newline
Rewrite the following polynomial in standard form.
\newline
x
−
9
+
x
2
2
x-9+\frac{x^{2}}{2}
x
−
9
+
2
x
2
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
Answer:
\newline
Submit Ansurer
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Question
\newline
Rewrite the following polynomial in standard form.
\newline
x
−
9
+
x
2
2
x-9+\frac{x^{2}}{2}
x
−
9
+
2
x
2
\newline
Answer Attempt
1
1
1
out of
2
2
2
\newline
Answer:
\newline
Submit Answer
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Which of the following equations could represent the polynomial graphed in the
x
y
x y
x
y
-plane?
\newline
Choose
1
1
1
answer:
\newline
(A)
y
=
x
(
x
+
2
)
(
x
−
6
)
y=x(x+2)(x-6)
y
=
x
(
x
+
2
)
(
x
−
6
)
\newline
(B)
y
=
x
(
x
−
2
)
(
x
+
6
)
y=x(x-2)(x+6)
y
=
x
(
x
−
2
)
(
x
+
6
)
\newline
(C)
y
=
(
x
+
2
)
(
x
2
−
2
x
−
3
)
y=(x+2)\left(x^{2}-2 x-3\right)
y
=
(
x
+
2
)
(
x
2
−
2
x
−
3
)
\newline
(D)
y
=
(
x
−
2
)
(
x
2
+
2
x
+
3
)
y=(x-2)\left(x^{2}+2 x+3\right)
y
=
(
x
−
2
)
(
x
2
+
2
x
+
3
)
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f
(
x
)
=
13
−
x
f(x)=13-x
f
(
x
)
=
13
−
x
\newline
h
(
x
)
=
x
2
−
6
x
−
18
h(x)=x^{2}-6 x-18
h
(
x
)
=
x
2
−
6
x
−
18
\newline
Write
(
f
∘
h
)
(
x
)
(f \circ h)(x)
(
f
∘
h
)
(
x
)
as an expression in terms of
x
x
x
\newline
(
f
∘
h
)
(
x
)
=
(f \circ h)(x)=
(
f
∘
h
)
(
x
)
=
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Perform the indicated operations & simplify.
\newline
Add:
\newline
(
4
−
−
9
)
+
(
−
12
+
−
16
)
(4-\sqrt{-9})+(-12+\sqrt{-16})
(
4
−
−
9
)
+
(
−
12
+
−
16
)
\newline
sum
=
\text{sum} =
sum
=
\newline
Subtract:
\newline
(
4
−
−
9
)
−
(
−
12
+
−
16
)
(4-\sqrt{-9})-(-12+\sqrt{-16})
(
4
−
−
9
)
−
(
−
12
+
−
16
)
\newline
difference
=
\text{difference} =
difference
=
\newline
Question Help:
\newline
□
\square
□
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B)
4
2
x
−
1
=
3
x
+
2
4^{2x-1}=3^{x+2}
4
2
x
−
1
=
3
x
+
2
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Given that
f
(
x
)
=
x
2
−
2
x
−
15
f(x)=x^{2}-2 x-15
f
(
x
)
=
x
2
−
2
x
−
15
and
g
(
x
)
=
x
+
3
g(x)=x+3
g
(
x
)
=
x
+
3
, find
f
(
x
)
+
g
(
x
)
f(x)+g(x)
f
(
x
)
+
g
(
x
)
and express the result as a polynomial in simplest form.
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