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Math Problems
Algebra 1
Domain and range of quadratic functions: equations
For each function, state whether it is linear, quadratic, or exponential.
\newline
\newline
Function
1
1
1
\newline
Function
2
2
2
\newline
Function
3
3
3
\newline
\newline
x
x
x
\newline
y
y
y
\newline
x
x
x
\newline
y
y
y
\newline
x
x
x
\newline
y
y
y
\newline
\newline
3
3
3
\newline
35
35
35
\newline
1
1
1
\newline
9
9
9
\newline
y
y
y
0
0
0
\newline
y
y
y
1
1
1
\newline
\newline
y
y
y
2
2
2
\newline
y
y
y
3
3
3
\newline
y
y
y
0
0
0
\newline
y
y
y
5
5
5
\newline
3
3
3
\newline
y
y
y
7
7
7
\newline
\newline
y
y
y
8
8
8
\newline
y
y
y
9
9
9
\newline
3
3
3
\newline
9
9
9
\newline
y
y
y
2
2
2
\newline
x
x
x
3
3
3
\newline
\newline
x
x
x
4
4
4
\newline
x
x
x
5
5
5
\newline
\bar{
4
4
4
}\(\newline\)\(x\)\(6\)\(\newline\)\bar{\(5\)}
\newline
\newline
y
y
y
5
5
5
\newline
x
x
x
8
8
8
\newline
x
x
x
9
9
9
\newline
y
y
y
3
3
3
\newline
\bar{
6
6
6
}$\(\newline\)\(y\)\(1\)\(\newline\)\(\newline\)Linear\(\newline\)Linear\(\newline\)Linear\(\newline\)Quadratic\(\newline\)Quadratic\(\newline\)Quadratic\(\newline\)Exponential\(\newline\)Exponential\(\newline\)Exponential\(\newline\)None of the above\(\newline\)None of the above\(\newline\)None of the above
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For each function, state whether it is linear, quadratic, or exponential.
\newline
\newline
Function
1
1
1
\newline
Function
2
2
2
\newline
Function
3
3
3
\newline
\newline
x
x
x
\newline
y
y
y
\newline
x
x
x
\newline
y
y
y
\newline
x
x
x
\newline
y
y
y
\newline
\newline
3
3
3
\newline
35
35
35
\newline
1
1
1
\newline
9
9
9
\newline
y
y
y
0
0
0
\newline
y
y
y
1
1
1
\newline
\newline
y
y
y
2
2
2
\newline
y
y
y
3
3
3
\newline
y
y
y
0
0
0
\newline
y
y
y
5
5
5
\newline
3
3
3
\newline
y
y
y
7
7
7
\newline
\newline
y
y
y
8
8
8
\newline
y
y
y
9
9
9
\newline
3
3
3
\newline
9
9
9
\newline
y
y
y
2
2
2
\newline
x
x
x
3
3
3
\newline
\newline
x
x
x
4
4
4
\newline
x
x
x
5
5
5
\newline
\bar{
4
4
4
}\(\newline\)\(x\)\(6\)\(\newline\)\bar{\(5\)}
\newline
\newline
y
y
y
5
5
5
\newline
x
x
x
8
8
8
\newline
x
x
x
9
9
9
\newline
y
y
y
3
3
3
\newline
\bar{
6
6
6
}$\(\newline\)\(y\)\(1\)\(\newline\)\(\newline\)Linear\(\newline\)Linear\(\newline\)Linear\(\newline\)Quadratic\(\newline\)Quadratic\(\newline\)Quadratic\(\newline\)Exponential\(\newline\)Exponential\(\newline\)Exponential\(\newline\)None of the above\(\newline\)None of the above\(\newline\)None of the above
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Find the domain of the function
f
(
x
)
=
1
2
−
2
x
−
x
2
f(x)=\frac{1}{\sqrt{2-2 x-x^{2}}}
f
(
x
)
=
2
−
2
x
−
x
2
1
. (Enter your answer using interval notation.)
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What is the image of a circle with equation
(
x
+
2
)
2
+
(
y
−
2
)
2
=
1
(x + 2)^2 + (y - 2)^2=1
(
x
+
2
)
2
+
(
y
−
2
)
2
=
1
when it is rotated through
π
6
\frac{\pi}{6}
6
π
about the origin?
\newline
(a)
(
x
+
(
3
+
1
)
)
2
+
(
y
−
(
3
−
1
)
)
2
=
1
(x + (\sqrt{3} + 1))^2 + (y - ( \sqrt{3} - 1))^2 = 1
(
x
+
(
3
+
1
)
)
2
+
(
y
−
(
3
−
1
)
)
2
=
1
\newline
(b)
(
x
−
(
3
+
1
)
)
2
+
(
y
+
(
3
−
1
)
)
2
=
1
(x - ( \sqrt{3} + 1))^2 + (y + (\sqrt{3} - 1))^2 = 1
(
x
−
(
3
+
1
)
)
2
+
(
y
+
(
3
−
1
)
)
2
=
1
\newline
(c)
(
x
+
(
3
−
1
)
)
2
+
(
y
−
(
3
+
1
)
)
2
=
1
(x + (\sqrt{3} - 1))^2 + (y - ( \sqrt{3} + 1))^2 = 1
(
x
+
(
3
−
1
)
)
2
+
(
y
−
(
3
+
1
)
)
2
=
1
\newline
(d)
(
x
−
(
3
−
1
)
)
2
+
(
y
+
(
3
+
1
)
)
2
=
1
(x - ( \sqrt{3} - 1))^2 + (y + (\sqrt{3} + 1))^2 = 1
(
x
−
(
3
−
1
)
)
2
+
(
y
+
(
3
+
1
)
)
2
=
1
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24
24
24
. Which function represents a quadratic function whose graph has a range of
{
y
∣
y
≥
3
}
\{y \mid y \geq 3\}
{
y
∣
y
≥
3
}
?
\newline
(A)
f
(
x
)
=
x
2
−
6
x
+
3
f(x)=x^{2}-6 x+3
f
(
x
)
=
x
2
−
6
x
+
3
\newline
(B)
f
(
x
)
=
x
2
−
3
f(x)=x^{2}-3
f
(
x
)
=
x
2
−
3
\newline
(C)
f
(
x
)
=
x
2
+
3
f(x)=x^{2}+3
f
(
x
)
=
x
2
+
3
\newline
(D)
f
(
x
)
=
x
2
+
6
x
+
3
f(x)=x^{2}+6 x+3
f
(
x
)
=
x
2
+
6
x
+
3
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Problem
1
1
1
Find the sum of all natural numbers that make the expression
384
−
12
n
\sqrt{384 - 12n}
384
−
12
n
an integer.
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A
∪
B
,
A
=
All real numbers
,
B
=
Even and prime
A \cup B, A=\text{All real numbers} , B=\text{Even and prime}
A
∪
B
,
A
=
All real numbers
,
B
=
Even and prime
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A part of quadratic iunction
f
f
f
is graphed on the grid.
\newline
What is the domain of the part of the function shown?
\newline
A All real numbers greater than or equal to
−
1
-1
−
1
\newline
(B) All real numbers greater than or equal to
1
1
1
\newline
(c) All real numbers
\newline
(
6
6
6
. All real numbers greater than or equal to
−
1
-1
−
1
and less than or equal to
5
5
5
\newline
(
1
1
1
) A
\newline
B
\newline
C
\newline
D
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find the average of
y
=
x
2
y=x^2
y
=
x
2
on
[
0
;
6
]
[0;6]
[
0
;
6
]
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The given function is:
G
(
x
)
=
x
x
−
x
x
−
1
G(x) = \frac{x\sqrt{x} - \sqrt{x}}{x - 1}
G
(
x
)
=
x
−
1
x
x
−
x
Let's find the domain and range of this function.
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Determine the domain of the following graph:
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f
(
x
)
=
(
5
x
+
3
)
(
x
−
2
)
(
3
x
+
7
)
(
x
+
5
)
f(x)=(5 x+3)(x-2)(3 x+7)(x+5)
f
(
x
)
=
(
5
x
+
3
)
(
x
−
2
)
(
3
x
+
7
)
(
x
+
5
)
has zeros at
x
=
−
5
,
x
=
−
7
3
,
x
=
−
3
5
x=-5, x=-\frac{7}{3}, x=-\frac{3}{5}
x
=
−
5
,
x
=
−
3
7
,
x
=
−
5
3
, and
x
=
2
x=2
x
=
2
.
\newline
What is the sign of
f
f
f
on the interval
−
7
3
<
x
<
−
3
5
-\frac{7}{3}<x<-\frac{3}{5}
−
3
7
<
x
<
−
5
3
?
\newline
Choose
1
1
1
answer:
\newline
(A)
f
f
f
is always positive on the interval.
\newline
(B)
f
f
f
is always negative on the interval.
\newline
(C)
f
f
f
is sometimes positive and sometimes negative on the interval.
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The function
f
f
f
is defined as
f
(
x
)
=
x
2
−
1
f(x)=x^{2}-1
f
(
x
)
=
x
2
−
1
.
\newline
What is the
x
x
x
-coordinate of the point on the function's graph that is closest to the origin?
\newline
Choose all answers that apply:
\newline
A
−
3
3
-\frac{\sqrt{3}}{3}
−
3
3
\newline
B
−
2
2
-\frac{\sqrt{2}}{2}
−
2
2
\newline
c
0
0
0
\newline
D
3
3
\frac{\sqrt{3}}{3}
3
3
\newline
E
2
2
\frac{\sqrt{2}}{2}
2
2
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An operation is defined on any three real numbers by
r
⊕
s
⊕
t
=
r
s
−
2
t
r \oplus s \oplus t=r^{s-2 t}
r
⊕
s
⊕
t
=
r
s
−
2
t
. If
3
⊕
5
⊕
m
=
81
3 \oplus 5 \oplus m=81
3
⊕
5
⊕
m
=
81
, then
m
=
m=
m
=
?
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he function below. Then, identify the domain, range, and the location and type
0
0
0
nuities.
\newline
Domain:
\newline
Range:
\newline
Discontinuities:
\newline
functions below, find
(
g
−
f
)
(
x
)
(g-f)(x)
(
g
−
f
)
(
x
)
\newline
8
8
8
.
\newline
Given the functions below, find and give its domain. its domain.
\newline
+
2
x
2
−
7
x
−
1
;
g
(
x
)
=
x
3
−
x
2
+
4
x
f
(
x
)
=
2
x
+
5
;
g
(
x
)
=
1
x
+2 x^{2}-7 x-1 ; g(x)=x^{3}-x^{2}+4 x \quad f(x)=\frac{2}{x+5} ; g(x)=\frac{1}{x}
+
2
x
2
−
7
x
−
1
;
g
(
x
)
=
x
3
−
x
2
+
4
x
f
(
x
)
=
x
+
5
2
;
g
(
x
)
=
x
1
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Between which two integers is the value?
\newline
−
90
-\sqrt{90}
−
90
\newline
the value is larger than
\qquad
and smaller than
\qquad
(be careful of this one...)
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The set
S
=
{
x
∣
−
3
<
x
<
4
}
S=\{x \mid-3<x<4\}
S
=
{
x
∣
−
3
<
x
<
4
}
is described by which interval notation?
\newline
[
−
3
,
4
]
[-3,4]
[
−
3
,
4
]
\newline
(
−
3
,
4
]
(-3,4]
(
−
3
,
4
]
\newline
[
−
3
,
4
[-3,4
[
−
3
,
4
)
\newline
(
−
3
,
4
)
(-3,4)
(
−
3
,
4
)
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What is the range of this quadratic function?
\newline
y
=
x
2
+
14
x
+
49
y = x^2 + 14x + 49
y
=
x
2
+
14
x
+
49
\newline
Choices:
\newline
(A)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(B)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(C)
y
∣
y
≥
−
7
{y | y \geq -7}
y
∣
y
≥
−
7
\newline
(D)all real numbers
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What is the domain of this quadratic function?
\newline
y
=
x
2
−
2
x
+
1
y = x^2 - 2x + 1
y
=
x
2
−
2
x
+
1
\newline
Choices:
\newline
(A)
{
x
∣
x
≤
1
}
\{x | x \leq 1\}
{
x
∣
x
≤
1
}
\newline
(B)
{
x
∣
x
≥
1
}
\{x | x \geq 1\}
{
x
∣
x
≥
1
}
\newline
(C)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(D)all real numbers
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What is the domain of this quadratic function?
\newline
y
=
x
2
+
2
x
−
24
y = x^2 + 2x - 24
y
=
x
2
+
2
x
−
24
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
−
25
}
\{x | x \geq -25\}
{
x
∣
x
≥
−
25
}
\newline
(B)
{
x
∣
x
≤
−
1
}
\{x | x \leq -1\}
{
x
∣
x
≤
−
1
}
\newline
(C)
{
x
∣
x
≥
−
1
}
\{x | x \geq -1\}
{
x
∣
x
≥
−
1
}
\newline
(D)all real numbers
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What is the domain of this quadratic function?
\newline
y
=
x
2
−
12
x
+
36
y = x^2 - 12x + 36
y
=
x
2
−
12
x
+
36
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(B)
{
x
∣
x
≥
6
}
\{x | x \geq 6\}
{
x
∣
x
≥
6
}
\newline
(C)
{
x
∣
x
≤
0
}
\{x | x \leq 0\}
{
x
∣
x
≤
0
}
\newline
(D)all real numbers
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What is the domain of this quadratic function?
\newline
y
=
x
2
−
6
x
−
40
y = x^2 - 6x - 40
y
=
x
2
−
6
x
−
40
\newline
Choices:
\newline
(A)
{
x
∣
x
≤
3
}
\{x | x \leq 3\}
{
x
∣
x
≤
3
}
\newline
(B)
{
x
∣
x
≥
3
}
\{x | x \geq 3\}
{
x
∣
x
≥
3
}
\newline
(C)
{
x
∣
x
≥
−
49
}
\{x | x \geq -49\}
{
x
∣
x
≥
−
49
}
\newline
(D)all real numbers
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What is the range of this quadratic function?
\newline
y
=
x
2
−
12
x
+
35
y = x^2 - 12x + 35
y
=
x
2
−
12
x
+
35
\newline
Choices:
\newline
(A)
y
∣
y
≥
6
{y | y \geq 6}
y
∣
y
≥
6
\newline
(B)
y
∣
y
≥
−
1
{y | y \geq -1}
y
∣
y
≥
−
1
\newline
(C)
y
∣
y
≤
−
1
{y | y \leq -1}
y
∣
y
≤
−
1
\newline
(D)all real numbers
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What is the range of this quadratic function?
\newline
y
=
x
2
−
12
x
+
27
y = x^2 - 12x + 27
y
=
x
2
−
12
x
+
27
\newline
Choices:
\newline
(A)
y
∣
y
≥
9
{y | y \geq 9}
y
∣
y
≥
9
\newline
(B)
y
∣
y
≥
6
{y | y \geq 6}
y
∣
y
≥
6
\newline
(C)
y
∣
y
≥
−
9
{y | y \geq -9}
y
∣
y
≥
−
9
\newline
(D)all real numbers
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What is the range of this quadratic function?
\newline
y
=
x
2
+
2
x
−
15
y = x^2 + 2x - 15
y
=
x
2
+
2
x
−
15
\newline
Choices:
\newline
(A)
y
∣
y
≥
−
16
{y | y \geq -16}
y
∣
y
≥
−
16
\newline
(B)
y
∣
y
≤
−
16
{y | y \leq -16}
y
∣
y
≤
−
16
\newline
(C)
y
∣
y
≥
−
1
{y | y \geq -1}
y
∣
y
≥
−
1
\newline
(D)all real numbers
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What is the range of this quadratic function?
\newline
y
=
x
2
−
14
x
+
49
y = x^2 - 14x + 49
y
=
x
2
−
14
x
+
49
\newline
Choices:
\newline
(A)
{
y
∣
y
≤
−
7
}
\{y | y \leq -7\}
{
y
∣
y
≤
−
7
}
\newline
(B)
{
y
∣
y
≥
−
7
}
\{y | y \geq -7\}
{
y
∣
y
≥
−
7
}
\newline
(C)
{
y
∣
y
≥
0
}
\{y | y \geq 0\}
{
y
∣
y
≥
0
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
4
y = x^2 - 4
y
=
x
2
−
4
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(B)
{
x
∣
x
≤
0
}
\{x | x \leq 0\}
{
x
∣
x
≤
0
}
\newline
(C)
{
x
∣
x
≥
−
4
}
\{x | x \geq -4\}
{
x
∣
x
≥
−
4
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
2
x
−
15
y = x^2 - 2x - 15
y
=
x
2
−
2
x
−
15
\newline
Choices:
\newline
(A)
{
x
∣
x
≤
1
}
\{x | x \leq 1\}
{
x
∣
x
≤
1
}
\newline
(B)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(C)
{
x
∣
x
≥
−
16
}
\{x | x \geq -16\}
{
x
∣
x
≥
−
16
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
12
x
+
32
y = x^2 - 12x + 32
y
=
x
2
−
12
x
+
32
\newline
Choices:
\newline
(A)
y
∣
y
≥
−
4
{y | y \geq -4}
y
∣
y
≥
−
4
\newline
(B)
y
∣
y
≥
4
{y | y \geq 4}
y
∣
y
≥
4
\newline
(C)
y
∣
y
≥
6
{y | y \geq 6}
y
∣
y
≥
6
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
2
x
−
35
y = x^2 + 2x - 35
y
=
x
2
+
2
x
−
35
\newline
Choices:
\newline
(A)
{
y
∣
y
≤
−
1
}
\{y | y \leq -1\}
{
y
∣
y
≤
−
1
}
\newline
(B)
{
y
∣
y
≥
−
1
}
\{y | y \geq -1\}
{
y
∣
y
≥
−
1
}
\newline
(C)
{
y
∣
y
≥
−
36
}
\{y | y \geq -36\}
{
y
∣
y
≥
−
36
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
12
x
+
20
y = x^2 + 12x + 20
y
=
x
2
+
12
x
+
20
\newline
Choices:
\newline
(A)
{
y
∣
y
≤
−
6
}
\{y | y \leq -6\}
{
y
∣
y
≤
−
6
}
\newline
(B)
{
y
∣
y
≥
−
6
}
\{y | y \geq -6\}
{
y
∣
y
≥
−
6
}
\newline
(C)
{
y
∣
y
≥
−
16
}
\{y | y \geq -16\}
{
y
∣
y
≥
−
16
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
6
x
+
8
y = x^2 - 6x + 8
y
=
x
2
−
6
x
+
8
\newline
Choices:
\newline
(A)
{
x
∣
x
≤
3
}
\{x | x \leq 3\}
{
x
∣
x
≤
3
}
\newline
(B)
{
x
∣
x
≥
3
}
\{x | x \geq 3\}
{
x
∣
x
≥
3
}
\newline
(C)
{
x
∣
x
≥
−
1
}
\{x | x \geq -1\}
{
x
∣
x
≥
−
1
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
8
x
+
16
y = x^2 - 8x + 16
y
=
x
2
−
8
x
+
16
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
4
}
\{x | x \geq 4\}
{
x
∣
x
≥
4
}
\newline
(B)
{
x
∣
x
≤
4
}
\{x | x \leq 4\}
{
x
∣
x
≤
4
}
\newline
(C)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
2
x
+
1
y = x^2 + 2x + 1
y
=
x
2
+
2
x
+
1
\newline
Choices:
\newline
(A)
y
∣
y
≥
1
{y | y \geq 1}
y
∣
y
≥
1
\newline
(B)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(C)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
2
x
−
24
y = x^2 - 2x - 24
y
=
x
2
−
2
x
−
24
\newline
Choices:
\newline
(A)
y
∣
y
≤
−
25
{y | y \leq -25}
y
∣
y
≤
−
25
\newline
(B)
y
∣
y
≥
1
{y | y \geq 1}
y
∣
y
≥
1
\newline
(C)
y
∣
y
≥
−
25
{y | y \geq -25}
y
∣
y
≥
−
25
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
4
x
+
4
y = x^2 + 4x + 4
y
=
x
2
+
4
x
+
4
\newline
Choices:
\newline
(A)
y
∣
y
≥
−
2
{y | y \geq -2}
y
∣
y
≥
−
2
\newline
(B)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(C)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
16
x
+
64
y = x^2 - 16x + 64
y
=
x
2
−
16
x
+
64
\newline
Choices:
\newline
(A)
x
∣
x
≥
8
{x | x \geq 8}
x
∣
x
≥
8
\newline
(B)
x
∣
x
≤
8
{x | x \leq 8}
x
∣
x
≤
8
\newline
(C)
x
∣
x
≥
0
{x | x \geq 0}
x
∣
x
≥
0
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
+
10
x
+
24
y = x^2 + 10x + 24
y
=
x
2
+
10
x
+
24
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
−
1
}
\{x | x \geq -1\}
{
x
∣
x
≥
−
1
}
\newline
(B)
{
x
∣
x
≥
−
5
}
\{x | x \geq -5\}
{
x
∣
x
≥
−
5
}
\newline
(C)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
16
x
+
64
y = x^2 + 16x + 64
y
=
x
2
+
16
x
+
64
\newline
Choices:
\newline
(A)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(B)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(C)
y
∣
y
≥
−
8
{y | y \geq -8}
y
∣
y
≥
−
8
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
6
x
+
9
y = x^2 - 6x + 9
y
=
x
2
−
6
x
+
9
\newline
Choices:
\newline
(A)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(B)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(C)
y
∣
y
≥
−
3
{y | y \geq -3}
y
∣
y
≥
−
3
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
10
x
+
25
y = x^2 - 10x + 25
y
=
x
2
−
10
x
+
25
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
5
}
\{x | x \geq 5\}
{
x
∣
x
≥
5
}
\newline
(B)
{
x
∣
x
≤
5
}
\{x | x \leq 5\}
{
x
∣
x
≤
5
}
\newline
(C)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
4
x
+
4
y = x^2 - 4x + 4
y
=
x
2
−
4
x
+
4
\newline
Choices:
\newline
(A)
y
∣
y
≥
2
{y | y \geq 2}
y
∣
y
≥
2
\newline
(B)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(C)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
8
x
−
20
y = x^2 - 8x - 20
y
=
x
2
−
8
x
−
20
\newline
Choices:
\newline
(A)
x
∣
x
≥
−
36
{x | x \geq -36}
x
∣
x
≥
−
36
\newline
(B)
x
∣
x
≤
4
{x | x \leq 4}
x
∣
x
≤
4
\newline
(C)
x
∣
x
≥
0
{x | x \geq 0}
x
∣
x
≥
0
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
+
12
x
+
36
y = x^2 + 12x + 36
y
=
x
2
+
12
x
+
36
\newline
Choices:
\newline
(A)
{
x
∣
x
≤
0
}
\{x | x \leq 0\}
{
x
∣
x
≤
0
}
\newline
(B)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(C)
{
x
∣
x
≥
−
6
}
\{x | x \geq -6\}
{
x
∣
x
≥
−
6
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
4
x
−
12
y = x^2 - 4x - 12
y
=
x
2
−
4
x
−
12
\newline
Choices:
\newline
(A)
y
∣
y
≥
−
16
{y | y \geq -16}
y
∣
y
≥
−
16
\newline
(B)
y
∣
y
≥
2
{y | y \geq 2}
y
∣
y
≥
2
\newline
(C)
y
∣
y
≥
16
{y | y \geq 16}
y
∣
y
≥
16
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
2
x
−
3
y = x^2 + 2x - 3
y
=
x
2
+
2
x
−
3
\newline
Choices:
\newline
(A)
y
∣
y
≥
4
{y | y \geq 4}
y
∣
y
≥
4
\newline
(B)
y
∣
y
≥
−
4
{y | y \geq -4}
y
∣
y
≥
−
4
\newline
(C)
y
∣
y
≥
−
1
{y | y \geq -1}
y
∣
y
≥
−
1
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
+
6
x
+
9
y = x^2 + 6x + 9
y
=
x
2
+
6
x
+
9
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
−
3
}
\{x | x \geq -3\}
{
x
∣
x
≥
−
3
}
\newline
(B)
{
x
∣
x
≥
0
}
\{x | x \geq 0\}
{
x
∣
x
≥
0
}
\newline
(C)
{
x
∣
x
≤
−
3
}
\{x | x \leq -3\}
{
x
∣
x
≤
−
3
}
\newline
(D)all real numbers
Get tutor help
What is the domain of this quadratic function?
\newline
y
=
x
2
−
4
x
+
3
y = x^2 - 4x + 3
y
=
x
2
−
4
x
+
3
\newline
Choices:
\newline
(A)
{
x
∣
x
≥
−
1
}
\{x | x \geq -1\}
{
x
∣
x
≥
−
1
}
\newline
(B)
{
x
∣
x
≥
2
}
\{x | x \geq 2\}
{
x
∣
x
≥
2
}
\newline
(C)
{
x
∣
x
≤
2
}
\{x | x \leq 2\}
{
x
∣
x
≤
2
}
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
+
8
x
+
16
y = x^2 + 8x + 16
y
=
x
2
+
8
x
+
16
\newline
Choices:
\newline
(A)
y
∣
y
≥
0
{y | y \geq 0}
y
∣
y
≥
0
\newline
(B)
y
∣
y
≤
0
{y | y \leq 0}
y
∣
y
≤
0
\newline
(C)
y
∣
y
≥
−
4
{y | y \geq -4}
y
∣
y
≥
−
4
\newline
(D)all real numbers
Get tutor help
What is the range of this quadratic function?
\newline
y
=
x
2
−
8
x
+
12
y = x^2 - 8x + 12
y
=
x
2
−
8
x
+
12
\newline
Choices:
\newline
(A)
{
y
∣
y
≤
−
4
}
\{y | y \leq -4\}
{
y
∣
y
≤
−
4
}
\newline
(B)
{
y
∣
y
≥
4
}
\{y | y \geq 4\}
{
y
∣
y
≥
4
}
\newline
(C)
{
y
∣
y
≥
−
4
}
\{y | y \geq -4\}
{
y
∣
y
≥
−
4
}
\newline
(D)all real numbers
Get tutor help
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2
3
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