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Math Problems
Algebra 2
Write equations of parabolas in vertex form using properties
3
3
3
. Which of the following is the equation of the parabola described with vertex at
(
5
,
−
3
)
(5, -3)
(
5
,
−
3
)
, axis parallel to the
y
y
y
-axis and passing through the point
(
1
,
1
)
(1, 1)
(
1
,
1
)
?
\newline
(a)
(
x
−
5
)
2
=
4
(
y
+
3
)
(x - 5)^2 = 4(y + 3)
(
x
−
5
)
2
=
4
(
y
+
3
)
\newline
(b)
(
x
+
5
)
2
=
4
(
y
−
3
)
(x + 5)^2 = 4(y - 3)
(
x
+
5
)
2
=
4
(
y
−
3
)
\newline
(c)
(
y
+
3
)
2
=
4
(
x
−
5
)
(y + 3)^2 = 4(x - 5)
(
y
+
3
)
2
=
4
(
x
−
5
)
\newline
(d)
(
y
−
3
)
2
=
4
(
x
+
5
)
(y - 3)^2 = 4(x + 5)
(
y
−
3
)
2
=
4
(
x
+
5
)
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Which of the following is the equation of the parabola described with vertex at
(
5
,
−
3
)
(5, -3)
(
5
,
−
3
)
, axis parallel to the
y
y
y
-axis and passing through the point
(
1
,
1
)
(1, 1)
(
1
,
1
)
?
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Identify the translation of the figure with vertices
a
(
1
,
−
3
)
a (1 ,- 3)
a
(
1
,
−
3
)
,
b
(
3
,
2
)
b( 3,2)
b
(
3
,
2
)
c
(
−
5
,
4
)
c (- 5, 4)
c
(
−
5
,
4
)
and
D
(
6
,
−
6
)
D (6 ,- 6 )
D
(
6
,
−
6
)
along the vector
<
3
−
1
>
<3 - 1>
<
3
−
1
>
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Use the graph and the factor theorem to list the factors of
f
(
x
)
f(x)
f
(
x
)
.
\newline
For the toolbar, press
A
L
T
+
F
10
(
P
C
)
A L T+F 10(P C)
A
L
T
+
F
10
(
PC
)
or
A
L
T
+
F
N
+
F
10
(
M
a
c
)
A L T+F N+F 10(\mathrm{Mac})
A
L
T
+
FN
+
F
10
(
Mac
)
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
3
)
(0,-3)
(
0
,
−
3
)
and focus
(
0
,
4
)
(0,4)
(
0
,
4
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
3
)
(0,-3)
(
0
,
−
3
)
and focus
(
0
,
−
1
)
(0,-1)
(
0
,
−
1
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
2
)
(0,-2)
(
0
,
−
2
)
and focus
(
0
,
3
)
(0,3)
(
0
,
3
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
7
)
(0,-7)
(
0
,
−
7
)
and directrix
y
=
−
4
y = -4
y
=
−
4
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
8
)
(0,8)
(
0
,
8
)
and focus
(
0
,
7
)
(0,7)
(
0
,
7
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and directrix
y
=
−
3
y = -3
y
=
−
3
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
1
)
(0,-1)
(
0
,
−
1
)
and focus
(
0
,
4
)
(0,4)
(
0
,
4
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
4
)
(0,4)
(
0
,
4
)
and focus
(
0
,
0
)
(0,0)
(
0
,
0
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
6
)
(0,-6)
(
0
,
−
6
)
and directrix
y
=
−
7
y = -7
y
=
−
7
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
6
)
(0,-6)
(
0
,
−
6
)
and directrix
y
=
−
2
y = -2
y
=
−
2
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
2
)
(0,-2)
(
0
,
−
2
)
and directrix
y
=
−
9
y = -9
y
=
−
9
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and focus
(
0
,
−
2
)
(0,-2)
(
0
,
−
2
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and directrix
y
=
8
y = 8
y
=
8
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
2
)
(0,-2)
(
0
,
−
2
)
and directrix
y
=
6
y = 6
y
=
6
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
4
)
(0,4)
(
0
,
4
)
and focus
(
0
,
2
)
(0,2)
(
0
,
2
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
7
)
(0,7)
(
0
,
7
)
and focus
(
0
,
10
)
(0,10)
(
0
,
10
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and directrix
y
=
−
10
y = -10
y
=
−
10
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and directrix
y
=
3
y = 3
y
=
3
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and focus
(
0
,
9
)
(0,9)
(
0
,
9
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
8
)
(0,8)
(
0
,
8
)
and focus
(
0
,
9
)
(0,9)
(
0
,
9
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
8
)
(0,-8)
(
0
,
−
8
)
and focus
(
0
,
−
7
)
(0,-7)
(
0
,
−
7
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
4
)
(0,4)
(
0
,
4
)
and focus
(
0
,
7
)
(0,7)
(
0
,
7
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
5
)
(0,5)
(
0
,
5
)
and focus
(
0
,
7
)
(0,7)
(
0
,
7
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
7
)
(0,7)
(
0
,
7
)
and directrix
y
=
6
y = 6
y
=
6
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
1
)
(0,1)
(
0
,
1
)
and focus
(
0
,
3
)
(0,3)
(
0
,
3
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
2
)
(0,2)
(
0
,
2
)
and directrix
y
=
5
y = 5
y
=
5
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
7
)
(0,-7)
(
0
,
−
7
)
and directrix
y
=
−
5
y = -5
y
=
−
5
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
0
)
(0,0)
(
0
,
0
)
and focus
(
0
,
6
)
(0,6)
(
0
,
6
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
2
)
(0,-2)
(
0
,
−
2
)
and focus
(
0
,
−
8
)
(0,-8)
(
0
,
−
8
)
.
\newline
Simplify any fractions.
\newline
______
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Write the equation in vertex form for the parabola with vertex
(
0
,
−
5
)
(0,-5)
(
0
,
−
5
)
and focus
(
0
,
0
)
(0,0)
(
0
,
0
)
.
\newline
Simplify any fractions.
\newline
______
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The side length of a square is decreasing at a rate of
2
2
2
kilometers per hour.
\newline
At a certain instant, the side length is
9
9
9
kilometers.
\newline
What is the rate of change of the area of the square at that instant (in square kilometers per hour)?
\newline
Choose
1
1
1
answer:
\newline
(A)
−
81
-81
−
81
\newline
(B)
−
36
-36
−
36
\newline
(C)
−
4
-4
−
4
\newline
(D)
−
324
-324
−
324
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Find the
a
a
a
value of a parabola that has a vertex at
(
−
3
,
−
4
)
(-3,-4)
(
−
3
,
−
4
)
and the point
(
−
6
,
−
25
4
)
(-6,-\frac{25}{4})
(
−
6
,
−
4
25
)
that lies on the curve.
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1
1
1
. Find the values of
x
x
x
and
y
y
y
such that the number
56129137
X
51
Y
56129137 \mathrm{X} 51 \mathrm{Y}
56129137
X
51
Y
is divisible by
88
88
88
\newline
(a)
2
2
2
,
2
2
2
\newline
(b)
4
4
4
,
2
2
2
\newline
(c)
4
4
4
,
4
4
4
\newline
(d) none of these
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Write the equation in vertex form for the parabola with focus
(
7
,
15
4
)
\left(7, \frac{15}{4}\right)
(
7
,
4
15
)
and directrix
y
=
−
15
4
y=-\frac{15}{4}
y
=
−
4
15
.
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8
8
8
) Find the equation of the parabola that has the following properties:
\newline
- vertex:
V
=
(
0
,
0
)
V=(0,0)
V
=
(
0
,
0
)
\newline
- focus:
F
=
(
−
2
,
0
)
F=(-2,0)
F
=
(
−
2
,
0
)
Get tutor help
8
8
8
) Find the equation of the parabola that has the following properties:
\newline
- vertex:
V
=
(
0
,
0
)
V=(0,0)
V
=
(
0
,
0
)
\newline
- focus:
F
=
(
−
2
,
0
)
F=(-2,0)
F
=
(
−
2
,
0
)
\newline
Graph the parabola. Label the focus, vertex, and directrix.
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*com B Unit
4
4
4
Test*
\newline
Which of the following are examples of isometries? Pick all that apply (
1
1
1
point)
\newline
(i) parallelogram
E
F
G
H
→
EFGH \rightarrow
EFG
H
→
parallelogram
X
W
V
U
XWVU
X
WV
U
\newline
(ii) hexagon
C
D
E
F
G
H
⇒
CDEFGH \Rightarrow
C
D
EFG
H
⇒
hexagon
T
U
V
W
K
Y
TUVWKY
T
U
VW
K
Y
\newline
(iii) triangle
△
E
F
O
=
△
V
W
U
\triangle EFO = \triangle VWU
△
EFO
=
△
VW
U
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About how long, in inches, is the diagonal of a rectangle with side lengths of
7
7
7
and
13
13
13
inches?
\newline
F.
10
10
10
\newline
G.
15
15
15
\newline
H.
20
20
20
\newline
J.
120
120
120
\newline
K.
218
218
218
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Determine the equation of the parabola with vertex
(
−
8
,
5
)
(-8,5)
(
−
8
,
5
)
and directrix
y
=
−
3
y=-3
y
=
−
3
.
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