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Let’s check out your problem:
Given the function
f
f
f
, evaluate
f
(
−
1
)
,
f
(
0
)
,
f
(
2
)
f(-1), f(0), f(2)
f
(
−
1
)
,
f
(
0
)
,
f
(
2
)
, and
f
(
4
)
f(4)
f
(
4
)
.
\newline
f
(
x
)
=
{
x
2
−
3
a
m
p
;
if
x
l
t
;
2
4
+
∣
x
−
6
∣
a
m
p
;
if
x
≥
2
f(x)=\left\{\begin{array}{cc} x^{2}-3 & \text { if } x<2 \\ 4+|x-6| & \text { if } x \geq 2 \end{array}\right.
f
(
x
)
=
{
x
2
−
3
4
+
∣
x
−
6∣
am
p
;
if
x
am
p
;
if
x
≥
2
lt
;
2
\newline
f
(
−
1
)
a
m
p
;
=
f
(
0
)
a
m
p
;
=
f
(
2
)
a
m
p
;
=
f
(
4
)
a
m
p
;
=
\begin{aligned} f(-1) & =\ \\ f(0) & =\ \\ f(2) & =\ \\ f(4) & =\\ \end{aligned}
f
(
−
1
)
f
(
0
)
f
(
2
)
f
(
4
)
am
p
;
=
am
p
;
=
am
p
;
=
am
p
;
=
View step-by-step help
Home
Math Problems
Algebra 1
Transformations of quadratic functions
Full solution
Q.
Given the function
f
f
f
, evaluate
f
(
−
1
)
,
f
(
0
)
,
f
(
2
)
f(-1), f(0), f(2)
f
(
−
1
)
,
f
(
0
)
,
f
(
2
)
, and
f
(
4
)
f(4)
f
(
4
)
.
\newline
f
(
x
)
=
{
x
2
−
3
if
x
<
2
4
+
∣
x
−
6
∣
if
x
≥
2
f(x)=\left\{\begin{array}{cc} x^{2}-3 & \text { if } x<2 \\ 4+|x-6| & \text { if } x \geq 2 \end{array}\right.
f
(
x
)
=
{
x
2
−
3
4
+
∣
x
−
6∣
if
x
<
2
if
x
≥
2
\newline
f
(
−
1
)
=
f
(
0
)
=
f
(
2
)
=
f
(
4
)
=
\begin{aligned} f(-1) & =\ \\ f(0) & =\ \\ f(2) & =\ \\ f(4) & =\\ \end{aligned}
f
(
−
1
)
f
(
0
)
f
(
2
)
f
(
4
)
=
=
=
=
Determine
f
(
−
1
)
f(-1)
f
(
−
1
)
:
Determine which part of the piecewise function to use for
f
(
−
1
)
f(-1)
f
(
−
1
)
since -1 < 2, use
f
(
x
)
=
x
2
−
3
f(x) = x^2 - 3
f
(
x
)
=
x
2
−
3
.
\newline
Calculation:
f
(
−
1
)
=
(
−
1
)
2
−
3
=
1
−
3
=
−
2
f(-1) = (-1)^2 - 3 = 1 - 3 = -2
f
(
−
1
)
=
(
−
1
)
2
−
3
=
1
−
3
=
−
2
.
Determine
f
(
0
)
f(0)
f
(
0
)
:
Determine which part of the piecewise function to use for
f
(
0
)
f(0)
f
(
0
)
since 0 < 2, use
f
(
x
)
=
x
2
−
3
f(x) = x^2 - 3
f
(
x
)
=
x
2
−
3
.
\newline
Calculation:
f
(
0
)
=
0
2
−
3
=
0
−
3
=
−
3
f(0) = 0^2 - 3 = 0 - 3 = -3
f
(
0
)
=
0
2
−
3
=
0
−
3
=
−
3
.
Determine
f
(
2
)
f(2)
f
(
2
)
:
Determine which part of the piecewise function to use for
f
(
2
)
f(2)
f
(
2
)
since
2
≥
2
2 \geq 2
2
≥
2
, use
f
(
x
)
=
4
+
∣
x
−
6
∣
f(x) = 4 + |x - 6|
f
(
x
)
=
4
+
∣
x
−
6∣
.
\newline
Calculation:
f
(
2
)
=
4
+
∣
2
−
6
∣
=
4
+
4
=
8
f(2) = 4 + |2 - 6| = 4 + 4 = 8
f
(
2
)
=
4
+
∣2
−
6∣
=
4
+
4
=
8
.
Determine
f
(
4
)
f(4)
f
(
4
)
:
Determine which part of the piecewise function to use for
f
(
4
)
f(4)
f
(
4
)
since
4
≥
2
4 \geq 2
4
≥
2
, use
f
(
x
)
=
4
+
∣
x
−
6
∣
f(x) = 4 + |x - 6|
f
(
x
)
=
4
+
∣
x
−
6∣
.
\newline
Calculation:
f
(
4
)
=
4
+
∣
4
−
6
∣
=
4
+
2
=
6
f(4) = 4 + |4 - 6| = 4 + 2 = 6
f
(
4
)
=
4
+
∣4
−
6∣
=
4
+
2
=
6
.
More problems from Transformations of quadratic functions
Question
Solve by completing the square.
\newline
m
2
−
10
m
−
29
=
0
m^2 - 10m - 29 = 0
m
2
−
10
m
−
29
=
0
\newline
Write your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.
\newline
`m` = ____ or `m` = _____
Get tutor help
Posted 10 months ago
Question
Find
g
(
x
)
g(x)
g
(
x
)
, where
g
(
x
)
g(x)
g
(
x
)
is the translation
5
5
5
units up of
f
(
x
)
=
x
2
f(x)=x^2
f
(
x
)
=
x
2
.
\newline
Write your answer in the form
a
(
x
–
h
)
2
+
k
a(x–h)^2+k
a
(
x
–
h
)
2
+
k
, where
a
a
a
,
h
h
h
, and
k
k
k
are integers.
\newline
g
(
x
)
=
g(x)=
g
(
x
)
=
____
Get tutor help
Posted 10 months ago
Question
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
{
y
∣
y
≥
2
}
\left\{y \mid y \geq 2\right\}
{
y
∣
y
≥
2
}
\newline
{
y
∣
y
≤
0
}
\left\{y \mid y \leq 0\right\}
{
y
∣
y
≤
0
}
\newline
{
y
∣
y
≥
0
}
\left\{y \mid y \geq 0\right\}
{
y
∣
y
≥
0
}
\newline
all real numbers
\text{all real numbers}
all real numbers
Get tutor help
Posted 7 months ago
Question
Write the equation of the parabola that passes through the points
(
1
,
0
)
(1,0)
(
1
,
0
)
,
(
2
,
0
)
(2,0)
(
2
,
0
)
, and
(
3
,
–
16
)
(3,\text{–}16)
(
3
,
–
16
)
. Write your answer in the form
y
=
a
(
x
–
p
)
(
x
–
q
)
y = a(x – p)(x – q)
y
=
a
(
x
–
p
)
(
x
–
q
)
, where
a
a
a
,
p
p
p
, and
q
q
q
are integers, decimals, or simplified fractions.
\newline
______
Get tutor help
Posted 7 months ago
Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.
\newline
f
2
+
8
f
+
_
_
_
_
_
f^2 + 8f + \_\_\_\_\_
f
2
+
8
f
+
_____
Get tutor help
Posted 7 months ago
Question
Solve for
h
h
h
.
\newline
h
2
+
39
h
=
0
h^2 + 39h = 0
h
2
+
39
h
=
0
\newline
\newline
Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
\newline
h
=
h =
h
=
____
\newline
Get tutor help
Posted 7 months ago
Question
Write a quadratic function with zeros
−
9
-9
−
9
and
−
7
-7
−
7
.
\newline
Write your answer using the variable
x
x
x
and in standard form with a leading coefficient of
1
1
1
.
\newline
f
(
x
)
=
_
_
_
_
_
f(x) = \_\_\_\_\_
f
(
x
)
=
_____
Get tutor help
Posted 7 months ago
Question
Find the equation of the axis of symmetry for the parabola
y
=
x
2
y = x^2
y
=
x
2
.
\newline
Simplify any numbers and write them as proper fractions, improper fractions, or integers.
\newline
‾
\underline{\hspace{3cm}}
Get tutor help
Posted 7 months ago
Question
Find
g
(
x
)
g(x)
g
(
x
)
, where
g
(
x
)
g(x)
g
(
x
)
is the translation
8
8
8
units up of
f
(
x
)
=
x
2
f(x) = x^2
f
(
x
)
=
x
2
.
\newline
Write your answer in the form
a
(
x
–
h
)
2
+
k
a(x – h)^2 + k
a
(
x
–
h
)
2
+
k
, where
a
a
a
,
h
h
h
, and
k
k
k
are integers.
\newline
g
(
x
)
=
g(x) =
g
(
x
)
=
______
\newline
Get tutor help
Posted 7 months ago
Question
Solve for
x
x
x
.
\newline
x
2
=
1
x^2 = 1
x
2
=
1
\newline
\newline
Write your answer in simplified, rationalized form.
\newline
x
=
x =
x
=
______ or
x
=
x =
x
=
______
\newline
Get tutor help
Posted 7 months ago
Related topics
Algebra - Order of Operations
Algebra - Distributive Property
`X` and `Y` Axes
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Common Multiple
Geometry - Quadrant